x2+ y2 – 20x + 8y + 115 = 0 What is the center of this circle? What is the radius of this circle ? Question x2+ y2 – 20x + 8y + 115 = 0 What is the center of this circle? What is the radius of this circle ? in progress 0 Math Alaia 3 weeks 2021-11-18T13:32:47+00:00 2021-11-18T13:32:47+00:00 1 Answer 0 views 0

## Answers ( )

Answer:(10, – 4 ), r = 1

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 the radius

Given

x² + y² – 20x + 8y + 115 = 0

Collect the x- terms and collect the y- terms and subtract 115 from both sides.

x² – 20x + y² + 8y = – 115

Complete the square on both the x and y terms

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

x² + 2(- 10)x + 100 + y² + 2(4)y + 16 = – 115 + 100 + 16

(x – 10)² + (y + 4)² = 1 ← in standard form

with centre = (10, – 4 ) and radius = 1