Use the equation below to identify the value fo each variable for the circle. Standard form equation of a Circle (x-h)^2+(y-v)^2=r^2 (h,v) = center r = radius h= ??? v = ??? r =…

Question

Use the equation below to identify the value fo each variable for the circle.

Standard form equation of a Circle

`(x-h)^2+(y-v)^2=r^2`
(h,v) = center
r = radius

h= ???
v = ???
r = ???

Then, write the standard form equation of the circle.

Answer 1

The equation of the circle in standard form is: (x - 2)² + (y - 4)² = 9

Explanation:

* Lets revise the standard form of the equation of the circle

- If the center of the circle is point (h , v) and the radius of the

circle is r, then the standard form of the equation of the circle

is (x - h)² + (y - v)² = r²

- (x , y) a general point on the circle

* Lets look to the picture

- The center of the circle is point (2 , 4)

- The highest point on the circle is (2 , 7) and the lowest point

on the circle is (2 , 1)

∴ The diameter of the circle = 7 - 1 = 6

∵ The radius = 1/2 the diameter

∴ The radius of the circle = 1/2 × 6 = 3

* Now we can write the equation of the circle

∵ h = 2 and v = 4

∵ r = 3

∴ (x - 2)² + (y - 4)² = 3²

∴ The equation of the circle in standard form is:

(x - 2)² + (y - 4)² = 9