Question

Find the center of a circle with the equation:
x2+y2+10x−16y+75=0

Answer 1

Answer: (-5,8)

Step-by-step explanation: since the radius of a circle square root of 14 so

x² + y² + 10x − 16y + 75 = 0

x² +10x + y² − 16y = -75

x² +10x + 25 + y² − 16y + 64 = -75 + 25 + 64

(x + 5)² + (y − 8)² = 14

Answer 2

The center is

`(-5,8)`

Step-by-step explanation

The given circle has equation

`{x}^(2) + {y}^(2) + 10x - 16y + 75= 0`

An easy way to find the center is by comparing to the general equation of the circle

`{x}^(2) + {y}^(2) + 2gx + 2fy + c = 0`

where (-g,-f) is the center.

By comparing, we have

`2gx = 10x`

`\implies \: 2g = 10`

Divide both sides by 2.

`g = 5`

Also,

`2fy = - 16y`

`2f = - 16`

Divide both sides by 2

`f = - 8`

Therefore the center is

`(-5,- - 8) = (-5,8)`