Answer: (x + 4)^2 + (y - 3)^2 = 50
Explanation:
Given: x^2 + y^2 + 8x - 6y - 25 =0, which the general form of the circle.
Solution:
Complete the square formula: (x - h)^2 + (y - k)^2 = r^2
Group similar term together on the left side of the equation and move the constant to right side of the equation ( remember to change the sign of the constant.
x^2 + y^2 + 8x - 6y - 25 =0
x^2 + 8x + y^2 - 6y = 25
Complete the Square: (x^2 + 8x + _____) + (y^2 - 6y + _____) = 25
Take half of the coefficient of the linear term for each variable, square the quotient, and add the answer to both side of the equation.
half of the coefficient of the linear term: ( 8/2)^2 = 16 and (-6/2)^2 = 9
(x^2 + 8x + 16) + (y^2 - 6y + 9) = 25 + 16 + 9
Each quality is a trinomial square and need to be factored
(x + 4)^2 + (y - 3)^2 = 50