find the center and radius of the circle with equation: x^2+y^2+6x-4y-15=0

Expert Answers

An illustration of the letter 'A' in a speech bubbles

x^2 + y^2 + 6x - 4y - 15 = 0

First we need to rewrite the equation using the standard form for the circle:

( x-a)^2 + ( y-b)^2 = r^2    such that:

(a,b) is the center and r is the radius:

To rewrite the equation we need to complete the square:

==> (x^2 + 6x) + (y^2 - 4y) = 15

==> (x^2 + 6x + 9 -9 ) + ( y^2 - 4y -4 + 4) = 15

==> (x + 3)^2 - 9 + ( y-2)^2  + 4 = 15

==> (x+3)^2 + (y-2)^2 = 15 - 4 + 9

==> (x+3)^2 + (y-2)^2 = 20

Then the center is ( -3, 2)  and r= sqrt20= 2sqrt5

Approved by eNotes Editorial Team

Posted on

Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial