Question

What is the standard form of this equation of a circle?

Answer 1

x² + y² + 14x − 4y − 28 = 0

x² +14x +y² - 4y =28
x²+2*7x  +7² -7²  + y² - 2*2y +2² - 2² = 28
(x+7)² + (y-2)² -7²-2² =28
(x+7)² + (y-2)²=28+49+4

(x+7)² + (y-2)² =81 is the answer.

Answer 2

(x2 + 14x + 49) + (y2 − 4y + 4) − 28 = 49 + 4

(x + 7)2 + (y − 2)2 − 28 = 49 + 4

(x + 7)2 + (y − 2)2 = 49 + 4 + 28 = 81.