Find the center and the radius of the circle with equation?

Question

x^2+y^2+6x-10y-10=0

Answer 1

The Equation of a circle is

 

 

(X- h)² + (Y-K)² = r²

 

Where r= radius and (h,K) are the coordinates of the center of circle

Rewriting the given equation

 

X² +h² -2hX +Y² +K²-2KY -r² = X² +Y² +6X - 10Y -10

 

From this equation values of h,K and r can be found by method of comparing the coefficients 

 

Answer 2

I will rewrite this equation in standard form.  That will give you a clue.

 

x² + 6x + y² - 10y - 10 = 0

 

 

Add 9, add 25, and add 10 to both sides of the equation.

 

x² + 6x + 9 + (y² - 10y + 25) - 10  + 10 = 9 + 25 + 10

 

 

(x + 3)² + (y - 5)² = 44    ----> standard form

 

From this form, you can get the center and radius of the circle.