SOLUTION: please help me to solve this quadratic equation: Give the propeties for the equation x^2+y^2+8x-2y+15=0, center: here are the possible answers: a)(4,1) b)(-4,1) c)(-8,2)

Click here to see ALL problems on Trigonometry-basics

Question 244126: please help me to solve this quadratic equation:
Give the propeties for the equation x^2+y^2+8x-2y+15=0, center:
here are the possible answers:
a)(4,1)
b)(-4,1)
c)(-8,2)
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
x^2+y^2+8x-2y+15=0
(x^2+8x+16) + (y^2-2y+1) + 15 = 17
(x+4)^2 + (y-1)^2 = 2
Center is (-4,1)
radius is sqrt(2)

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

You need to complete the square on both and , then factor the perfect squares.

First, move the constant to the RHS:

Rearrange:

Divide the coefficient on the -term by 2, then square the result. Add this result to both sides of the equation.

Do the same thing for the -term:

Factor and and then replace these two trinomials in your equation with the squared binomial representation.

You can then determine the center by inspection since a circle centered at with radius is defined by:

Pay careful attention to the signs on your center coordinates.

John