Question

*30 points*

What is the equation of the circle in general
form?
x2 + y2 + 2x + 8y + 9 = 0
X2 + y2 – 2x– 8y + 9 = 0
X2 + y2 – 2x – 8y – 47 = 0
X2 + y2 + 2x + 8y – 47 = 0

Answer 1

Third one:

x² + y² - 2x - 8y - 47 = 0

Explanation:

Equation of circle:

(x - h)² + (y - k)² = r²

(x - 1)² + (y - 4)² = 8²

(x - 1)² + (y - 4)² = 64

x² - 2x + 1 + y² - 8y + 16 - 64 = 0

x² + y² - 2x - 8y - 47 = 0

Answer 2

x^2 + y^2 -2x -8y -47 =0

Explanation:

The center is at (1,4) and the radius is 8 units

We can write the equation as

(x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center and r is the radius

(x-1)^2 + (y-4)^2 = 8^2

Foil

x^2 -2x+1 + y^2 -8y +16 = 64

x^2 + y^2 -2x -8y +17 =64

Subtract 64 from each side

x^2 + y^2 -2x -8y +17-64 =64-64

x^2 + y^2 -2x -8y -47 =0