A circle with center (-2,6) passes through the point (-2,10). Which of the following is the equation of the circle?
Answers
If we plug x = -2 and y = 10 into equation a and c well see which one is correct
Plug in equation a:_
((-2+2)^2 + (10-6)^2 = 0 + 16 = 16
so its equation a Answer
First option is correct. The equation of the is [tex](x-2)^{2} +(y-6)^{2} =16[/tex].
What is circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called "center".
General equation for circle[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
where,
(h, k) is the coordinate of the center of a circle
(x, y) are the coordinate points
r is the radius of circle.
According to the question
we have
the center of the circle, (h, k) = (-2, 6)
and the circle passes through the point (-2, 10)
since, the circle passes through point (-2, 10), the radius(r) of the circle is the distance between the points (-2, 6) and (-2, 10)
⇒ [tex]r =\sqrt{(-2+2)^{2 }+ (6-10)^{2} }[/tex]
⇒ r = [tex]\sqrt{0^{2}+(-4)^{2} }[/tex]
⇒[tex]r = \sqrt{16}[/tex]
⇒[tex]r = 4unit[/tex]
therefore,
the equation of the circle is given by
[tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex]
[tex](x-(-2))^{2} +(y-6)^{2} =16[/tex]
[tex](x+2)^{2} +(y-6)^{2} =16[/tex] ..... (1)
[tex]x^{2} +4+4x+y^{2} +12y+36 = 16[/tex]
[tex]x^{2} +y^{2} +4x+12y+24=0[/tex]
Hence, equation 1 represent the equation of circle i.e. [tex](x+2)^{2} + (y-6)^{2} =16[/tex]
Learn more about the equation of circle here:
https://brainly.com/question/10618691
#SPJ2
Related Questions
What can be concluded about a cylinder and a cone with the same height and radius measures? Check all that apply.
A. The cone has the greater volume.
B. The cone and cylinder have the same base area.
C. The volume of the cone is 1/3 the volume of the cylinder.
D. The cylinder can fit inside the cone.
E. The cone and cylinder have the same diameter.
Answers
The cone has a greater volume than the cylinder, and their base areas are equal, but the cone's volume is 1/3 of the cylinder's volume.
A. The cone has the greater volume.
B. The cone and cylinder have the same base area.
C. The volume of the cone is 1/3 the volume of the cylinder.
You and a friend stand back to back. You run 20 feet forward then 15 feet to the right. At the same time, your friend runs 16 feet forward then 12 feet to her right. She stops and hits you with a snowball. How far does your friend throw the snowball?
Answers
From the figure below D is my position E is friend's position. The distance we are estimating is ED
ACE and ADB are assumed to be right angles.
c²=a²+b²
Thus the length of the hypotenuse made from the triangle movement I moved will be:
c²=20²+15²
c²=400+225
c²=625
c=25 ft
Length of the hypotenuse made by my friend will be:
c²=16²+12²
c²=256+144
c²=400
c=20 ft
The total distance the ball will be thrown will be:
20+25=45ft
Graph the solution to the scenario by dragging and dropping a circle/arrow onto the number line.
Billy's plant grows at least 2 inches a month.
Answers
Since his plant grows "at least" 2 inches per month, this means that it can grow that much or more. This is the same as the inequality "greater than or equal to."
Since the plant can grow 2 inches per month, the circle is filled in at 2. Since it can grow more than this, the arrow points to the right, which is the numbers greater than 2.
Answer:
The line going to the right with a filled in circle plotted on 2.
Step-by-step explanation:
I did the review test and got it right
Can anyone help? Please
Answers
650-50 = 600
The width of a large, rectangle-shaped tree farm is 1.9 kilometers. The best length of the farm is 4.4 kilometers. What is the best estimate of the area of the farm? Estimate 1.9 x 4.4
Answers
Since 1.9 is closest to 2 than it is to 1, the nearest integer of 1.9 is 2.
Similarly, since 4.4 is closest to 4 than it is to 5, the nearest integer of 4.4 is 4.
Now, to estimate the area of the farm, we are going to multiply our two integers:
Estimated Area of the Farm= [tex]2[/tex]x[tex]4=8[/tex]
Since 8 is between 4 and 10, we can conclude that the best estimate of the area of the farm is: between 4 and 10
Answer:
between 4 and 10
Step-by-step explanation:
i did the quiz.
if the length of an arc is 12π inches and the radius of the circle us 10 inches, what is the measure of the arc?
Answers
Thus, s = (12pi inches) = (10 inches)(theta), so
theta = the central angle (not the measure of the arc) = (12pi)/(10 inches), or
theta = 1.2*pi (no units of measurement)
Answer:
The measure of arc is 216°
Step-by-step explanation:
Length of arc, L = 12π inches
Radius of the circle, R = 10 inches
Formula: [tex]\theta=\dfrac{L}{R}[/tex]
Where, [tex]\theta[/tex] in radian.
By substituting L and R into formula.
[tex]\theta=\dfrac{12\pi}{10}[/tex]
[tex]\theta=\dfrac{6\pi}{5}[/tex]
Now we change radian to degree
[tex]\text{Degree }=\dfrac{\text{Radian}}{\pi}\times 180^\circ[/tex]
[tex]\text{Degree }=\dfrac{6\pi}{5\pi}\times 180^\circ[/tex]
Central angle = 216°
Hence, The measure of arc is 216°
How many sides does a regular polygon have if each exterior angle measures 30?
Answers
The number of sides that the polygon with each exterior angle measuring 30° has is 12.
What is a polygon?A polygon is a planar figure characterised by a limited number of straight-line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both.
The sum of all the exterior angles of a regular polygon is always equal to 360°. Therefore, the measure of an exterior angle for a regular polygon is given as,
[tex]\theta = \dfrac{360^o}{n}[/tex]
where n is the number of sides.
Given that the measure of the exterior angle is 30°. Therefore, the number of sides will be,
[tex]\theta = \dfrac{360^o}{n}\\\\ 30^o = \dfrac{360^o}{n}\\[/tex]
n = 12
Learn more about Polygon:
https://brainly.com/question/10441863
#SPJ5
Anne plans to increase the prices of all the items in her store but 5%. To the nearest cent how much will an artist saved if the artist buys a canvas and a frame that each measures 24 by 36 in before the price increase goes into effect. 24/36 canvas price 22.80 and the frame price is 89.98
Answers
The artist will not save any money, but will end up paying $24.06 more after the price increase.
Explanation:To find out how much the artist will save, we first need to calculate the original cost of the canvas and frame. The price of the canvas is $22.80 and the frame is $89.98. Next, we calculate the price increase of 5% for both the canvas and frame. To do this, we multiply the original prices by 0.05. After that, we add the price increase to the original prices to get the new prices. Finally, we subtract the new prices from the original prices to find the amount saved by the artist.
The calculations are as follows:
Canvas price increase: $22.80 x 0.05 = $1.14New canvas price: $22.80 + $1.14 = $23.94Frame price increase: $89.98 x 0.05 = $4.50New frame price: $89.98 + $4.50 = $94.48Amount saved: ($22.80 + $89.98) - ($23.94 + $94.48) = $94.36 - $118.42 = -$24.06The artist will actually end up paying $24.06 more after the price increase, rather than saving any money.
Learn more about price increase here:https://brainly.com/question/32987301
#SPJ12
From a barrel of colored marbles , you randomly select 5 blue , 2 yellow , 3 red , 4 green , and 2 purple marbles. Find the expreimetal probability of randomly selecting a marble that is NOT yellow .
1. 9 / 16
2. 7 / 8
3. 8 / 9
4. 3 / 4
Answers
Answer:
4/5
Step-by-step explanation:
From your experiment of drawing 20 marbles you now have a proportion of non-yellow marbles to total marbles and from that you can come up with an experimental probability that you'll draw a non-yellow marble.
P(not yellow) = 16/20
But that can be reduced by dividing top and bottom by 4:
Find total cost $20.20 and 40% off , tax is 6%
Answers
The price of an item has been reduced by 35%
. The original price was $71.
.
Answers
100 - 35 = 65
65% = 0.65
Multiply:
0.65 × 71 = 46.15
Hope this helped☺☺
Twenty-five percent of 66 is ______
Answers
original amount * percent change = your answer
How would you use a yardstick to measure the length of a rug
Answers
Hope this helps! :)
Liz is putting wallpaper on a 9-foot by 12foot wall. The roll of wallpaper is 30 inches wide. What is the area
Answers
9 × 12 = 108
The area of the wall is 108 ft².
Not sure what the width of the wallpaper is for <:(
A pie is cut into two equal pieces. Each of the pieces was cut into halves again and each of the smaller pieces was cut into two equal pieces. If two of the pieces of the pie are eaten what portion of the pie remains?
Answers
Answer:
→When, pie is cut into two equal pieces,
If represented in terms of fraction , value of each part
[tex]=\frac{1}{2}[/tex]
→Now, the two parts is cut into halves again, then in terms of fraction, each part will be represented as
[tex]=\frac{1}{2\times 2}\\\\=\frac{1}{4}[/tex]
→Now, the two parts is again,cut into halves again, then in terms of fraction, each part will be represented as
[tex]=\frac{1}{2\times 2 \times 2}\\\\=\frac{1}{8}[/tex]
→Now, two of the pieces of the pie are eaten,which will be equal to
[tex]=\frac{1}{8}+\frac{1}{8}\\\\=\frac{2}{8}\\\\=\frac{1}{4}[/tex]
⇒Portion of the pie which is remaining
[tex]=1-\frac{1}{4}\\\\=\frac{3}{4}[/tex]
How much greater is the median number of pairs of shoes in the inventory at the Golf Pro Shop than the median number of pairs of shoes in the inventory at the Tennis Pro Shop?
Please help, Thanks!
Answers
square root of 16 times the square root of 25
[tex] \sqrt{16} \times \sqrt{25} [/tex]
Answers
Short answer: 20
Why?
First, find the square root of each number. The square root of 16 is 4. The square root of 25 is 5. Multiply each number. 4 × 5 = 20
Hope this helped you! ♥
The probability of selecting the letter Z at random from the letters of the alphabet is 1 half 26.
A.Theoretical
B. Empirical
Answers
There is 1 "z" in the alphabet. Therefore the probability of choosing a "z" is 1/26
denominator vs numerator
Answers
What is the range of the function graphed below?
Answers
Option: C is the correct answer.
The range of the function which is graphed is:
C. All real numbers.
Step-by-step explanation:Domain of a function--
The domain of a function are the set of all the possible x values for which the function is defined.
Range of a function--
The range of a function are the set of all the possible values which are attained by a function in it's defined domain.
By looking at the graph of the given function we observe that the function is strictly increasing and it takes all the real values i.e. it takes all the values from (-∞,∞).
Hence, the answer is: Option: C
The smaller triangle was dilated to form the larger triangle. What is the value of x?
6.9
7.5
10
11
Answers
scale factor=measure larger triangle/measure smaller triangle---->18/12
scale factor=1.5
so
measure larger triangle=scale factor*measure smaller triangle
for the leg in the smaller triangle equal to 5
measure larger triangle=1.5*5-----> 7.5
the answer is
7.5
Answer:
7.5
Step-by-step explanation:
Can someone answer 14,15 and 16? Thank you!
Answers
15 = 8 pi/10 pi = 4/5
16 = no
24=12 18=9 14=7 8=4 6=?
Answers
Which is the equation in slope intercept form for the line that passes through (-2,4) and is parallel to 2x + y = 4
Answers
If lines L and M are parallel in the given diagram and angle 5 is 132°, what is the measure of angle 3?
Answers
The answer is 48 degrees.
How I got my answer:
Angle 5 + Angle 3 = 180(Co. Interior Angles)
let Angle 3 be x
132 + x = 180
x = 180 - 132
x = 48
The measure of Angle 3 is 48 degrees.
Hope this helps you.
Since lines L and M are parallel, corresponding angles such as angle 5 and angle 3 will be equal. Thus, if angle 5 is 132°, angle 3 will also be 132°.
Explanation:This question concerns parallel lines and the angles formed by a transversal cutting across them. The lines L and M in the given diagram are parallel. Parallel lines have a special property where corresponding angles are equal. If angle 5 measures 132°, then the corresponding angle, angle 3, also measures 132°, because of this property of parallel lines.
Learn more about Parallel Lines here:
https://brainly.com/question/32035102
#SPJ2
India can paint 3 ½ walls in one day. How many walls can she paint in 5 ½ days?
Answers
5.5 is the same thing as 5 1/2
3.5 walls/1 day
3.5 walls x 5.5 days = 19.25 walls
What is the surface area of the regular pyramid
Answers
WILL GIVE BRAINLIEST TO CORRECT ANSWER 15 POINTS
Two poles, AB and ED, are fixed to the ground with the help of ropes AC and EC, as shown: Two right triangles ABC and EDC have a common vertex C. Angle ABC and EDC are right angles. AB is labeled 11 feet, AC is labeled 13 feet, EC is labeled 10 feet, and ED is labeled 5 feet. What is the approximate distance, in feet, between the two poles?
Answers
Its 15.59, it corresponds with the other questions.The other answers never appear twice.
Answer:
15.59
Step-by-step explanation:
What percent of the June budget was for babysitting and movies (to the nearest tenth)?
Answers
Mortgage - $752 Tim's Chevron - $23Johnny's Allowance - $8Electric - $176Jenny-babysitting - $12Movie - $14Dry Cleaning - $41Tithe - $85,Credit Card - $150Food - $101Phone - $45Water - $16 Car - $272
Adding all the expenses, will give us a total of $1695.
To get the percent which is allocated for movie and the baby sitting:
Add the amount for the two then divide that to the total then multiply it by 100%
= 12 + 14 / 1695 x 100%
= 26 / 1695 x 100%
= 0.015339233 x 100%
=1.5%
The answer is 1.5%
William is reading a book for class . The book is 94 pages long . For the first assignment , William read 25 pages . For the second assignment , he read 37 pages . For the last assingment , he has to finish the book. How many pages does he have left to read
Answers
25 + 37 = 62
94 - 62 = 32 pages