Question

What is the equation of a circle with center (-4, 7) and radius 6?

A. (x - 4)2 + (y + 7)2 = 6
B. (x + 4)2 + (y - 7)2 = 36
C. (x + 4)2 + (y - 7)2 = 6
D. (x - 4)2 + (y + 7)2 = 36

Answer 1

B.

The equation of a circle is:
(x-h)^2 + (y-k)^2 = r^2 - where (h,k) is the centre and r is the radius

Therefore, a circle with centre (-4,7) and radius 6 has the equation:
(x-(-4))^2 + (y-7)^2 = (6)^2
(x+4)^2 + (y-7)^2 = 36

Answer 2

Answer: B.
`(x+4)^2+(y-7)^2=36`

Explanation:

We know that the equation of a circle having center at (h,k) and radius r is given by :-

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

Given : The center of the circle : (-4,7)

The radius of the circle : 6 units

Then the equation of a circle with center (-4, 7) and radius 6 will be :-

`(x-(-4))^2+(y-7)^2=6^2\\\\\Rightarrow\ (x+4)^2+(y-7)^2=36`