SOLUTION: Decide whether or not the equation has a circle as its graph. If it​ does, give the center and the radius. If it does​ not, describe the graph. x^2 + y^2 - 10x + 4y =

Algebra ->  Circles -> SOLUTION: Decide whether or not the equation has a circle as its graph. If it​ does, give the center and the radius. If it does​ not, describe the graph. x^2 + y^2 - 10x + 4y =      Log On


   

Question 1028941: Decide whether or not the equation has a circle as its graph. If it​ does, give the center
and the radius. If it does​ not, describe the graph.
x^2 + y^2 - 10x + 4y = -28
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Two things to think:
Coefficients of x^2 and y^2 must be equal, and standard form equation must have POSITIVE value for the constant member.

Difficult to know by just looking at your general form equation. If you have qualitative understanding of the general form equation, then you could use that. Otherwise, put the equation into standard form. This may require Completing the Square for x and for y.

x%5E2-10x%2By%5E2%2B4y=-28
x%5E2-10x%2B25%2By%5E2%2B4y%2B4=-28%2B25%2B4
%28x%5E2-10x%2B25%29%2B%28y%5E2%2B4y%2B4%29=1
%28x-5%29%5E2%2B%28y%2B2%29%5E2=1

Center (5,-2)
Radius size, 1