X^2+y^2-8x+8y+23=0

Question

Write equation in standard form. Cirles, identify the center and radius. Identify ellipses and hyperbole identify the center.

Answer 1

X² + y² - 8x + 8y + 23 = 0

 

The standard form is:

 

     (x-h)² + (y-k)² = r²

 

where (h,k) is the location of the circle's center and r is its radius.  To convert the equation you are given to standard form, you must to complete the square for both the x terms and the y terms:

 

     (x² - 8x + 16) + (y² + 8y + 16) = -23 + 16 + 16

 

     (x-4)² + (y+4)² = 9   (Standard Form)

 

So h = 4 and k = -4 and the center is located at (4,-4).  The radius = √9 = 3