Question

The equation of a circle is x^2+ y^2+8x - 10y + 5 = 0

What are the center and the radius of the circle? Show your work.

Answer 1

Explanation:

`{x}^(2) + 8x + {y}^(2) - 10y = - 5`

Complete the square for the x direction

For the x direction,

`{x}^(2) + 8x +( (8)/(2) ) {}^(2) + {y}^(2) - 10y + ( ( - 10)/(2) ) {}^(2) = - 5 + ( (8)/(2) ) {}^(2) + ( ( - 10)/(2) ) {}^(2)`

`{x}^(2) + 8x + 16 + {y}^(2) - 10y + 25 = - 5 + 16 + 25`

`(x + 4) {}^(2) + (y - 5) {}^(2) = 36`

The center is (-4,5) with a radius of 6.