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

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step-by-step explanation:

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