z^2+ y^2 + 8x – 16y + 31 = 0 What is the center of this circle ? What is the radius of this circle ? Question z^2+ y^2 + 8x – 16y + 31 = 0 What is the center of this circle ? What is the radius of this circle ? in progress 0 Math Delilah 4 weeks 2021-11-10T14:17:53+00:00 2021-11-10T14:17:53+00:00 1 Answer 0 views 0

## Answers ( )

Answer:(- 4, – 8 ), radius = 7

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 – 16y + 31 = 0

Collect the x- terms, collect the y- terms together and subtract 31 from both sides.

x² + 8x + y² – 16y = – 31

Use the method of completing the square on the x and y terms

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

x² + 2(4)x + 16 + y² + 2(- 8)y + 64 = – 31 + 16 + 64

(x + 4)² + (y – 8)² = 49 ← in standard form

with centre = (- 4, 8 ) and r = = 7