A circle has the equation x2+y2-8x-2y-17=0.

What is the equation of the circle in standard form?

(x-4) 2 + (y-1) 2=34

(x+4) 2 + (y-1) 2=34

(x-4) 2 + (y-1) 2=17

(x+4) 2 + (y-1) 2=17

A

Step-by-step 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

Given

x² + y² - 8x - 2y - 17 = 0

Collect the x - terms and the y - terms together and add 17 to both sides

x² - 8x + y² - 2y = 17

Use the method of completing the square on both x and y terms.

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

x² + 2 ( - 4) x + 16 + y² + 2 ( - 1) y + 1 = 17 + 16 + 1

(x - 4) ² + (y - 1) ² = 34 → A