Question

How is the equation of this circle written in standard form?

x2 + y2 - 6x + 14y = 142
A)
(x - 3)2 + (y + 7)2 = 200
B)
(x+ 3)2 + (y - 7)2 = 200
(x - 6)2 + (y + 14)2 = 142
D)
(x+6)2 + (y- 14)2 = 142

Answer 1

A

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.

To obtain this form use the method of completing the square.

Given

x² + y² - 6x + 14y = 142

Collect the x and y terms together

x² - 6x + y² + 14y = 142

add (half the coefficient of both x and y terms )² to both sides

x² + 2(- 3)x + 9 + y² + 2(7)y + 49 = 142 + 9 + 49

(x - 3)² + (y + 7)² = 200 → A