Question

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

Answer 1

(x - 6)² + (y + 4)² = 36

Explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (6, - 4) and r = 6, hence

(x - 6)² + (y - (- 4))² = 6², that is

(x - 6)² + (y + 4)² = 36 ← equation of circle

Answer 2

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

Explanation:

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

h=6

k=-4

r=6

`(x-6)^(2) + (y+4)^(2)=6^(2)`

`x^(2) -12x+36 + y^(2) +8y+16=36\\\\x^(2) +y^(2) -12x +8y +52-36 = 0\\\\x^(2) +y^(2) -12x +8y+ 16 = 0`