Question

3. Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact formx° + y? + 8x- 6y - 15 = 0

Answer 1

x^2 + y^2 + 8x- 6y - 15 = 0

We need to complete the square for each variable

x^2 +8x + y^2 - 6y - 15 = 0

Add 15 to each side

x^2 +8x + y^2 - 6y - 15+15 = 0+15

x^2 +8x + y^2 - 6y =15

x^2 + 8x + 16 + y^2 -6y + 9 = 15 + 16 + 9

( x+4 ) ^2 + (y-3)^2 = 40

This is the standard form for a circle

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

Rewriting

( x - -4) ^2 + ( y - 3) ^2 = (sqrt( 4*10))^2

( x - -4) ^2 + ( y - 3) ^2 = ( 2sqrt( 10))^2

The center is at ( -4, 3) and the radius is at 2 sqrt(10)