Question

What is the equation of a circle with center (-4,7) radius 3?

Answer 1

a. (x + 4)² + (y – 7)² = 3²

Explanation:

General equation for a circle is:

(x – h)² + (y – k)² = r²

h and k are the center (h, k), and r is the radius.

They want a center of (-4, 7) so h=-4 and k=7

They want a radius of 3 so r=3

plug it into the equation.

(x – h)² + (y – k)² = r²

(x – (-4))² + (y – (7))² = (3)²

(x + 4)² + (y – 7)² = 3²

Answer 2

Answer: ( x + 4 )² + ( y - 7 )² = 3²

Explanation:

Formula for the equation of a circle centre (a, b), radius r

= ( x - a )² + ( y - b )² = r²--------------------------------------------------------1

a = -4 and b = 7 while r = 3

Therefore substitute for a , b and r in the equation 1 above to get the equation of the circle.

( x - (-4 ) )² + ( y - 7 )² = 3²

open the brackets through direct or indirect methods gives

( x + 4 )² + ( y - 7 )² = 9

x² + 8x + 16 + y² - 14y + 49 = 9

x² + y² + 8x - 14y + 16 + 49 - 9 = 0

x² + y² + 8x - 14 y + 116 = 0