Question

Which of the following is the equation of the circle shown below?

A:(x+3)^2+(y-5)^2=8
B:(x+3)^2+(y-5)^2=64
C:(x-3)^2+(y+5)^2=64
D:(x-3)^2+(y+5)^2=8

Answer 1

Equation of circle:

(y-k)² + (x-h)² = r², k & h being the coordinate of the center

(y+5)² + (x-3)² = 64, that is C

Answer 2

Answer: C.
`(x-3)^2+(y+5)^2=64`

Explanation:

The general equation of a circle with center (h,k) and radius r is given by :-

`(x-h)^2+(y-k)^2=r^2`

From the given graph, the center of the circle is (3,-5) and the radius of the circle is 8 units.

Now, the equation of a circle with center (3,-5) and radius 8 units is given by :-

`(x-3)^2+(y-(-5))^2=(8)^2\\\\\Rightarrow\ (x-3)^2+(y+5)^2=64`

Hence, the equation of the given circle :
`(x-3)^2+(y+5)^2=64`