Question

The equation for a circle is ​x^2 − 8x + y^2 - 2y - 8 = 0

​ .

What is the equation of the circle in standard form?

(x−16)^2+(y−1)^2=16 (A)

(x−4)^2+(y−1)^2=25 (B)

(x−16)^2+(y−1)^2=25 (C)

(x−4)^2+(y−1)^2=16 (D)

Answer 1

B

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 - 8x + y² - 2y - 8 = 0 ( add 8 to both sides )

x² - 8x + y² - 2y = 8

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

x² + 2(- 4)x + 16 + y² + 2(- 1)y + 1 = 8 + 16 + 1

(x - 4)² + (y - 1)² = 25 → B