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+6x−10y

Algebra ->  Equations -> 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+6x−10y      Log On


   

Question 1085731: 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+6x−10y+38=0
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2By%5E2%2B6x%26%238722%3B10y%2B38=0+...to check if it is a circle, write the equation in form %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2
x%5E2%2B6x%2By%5E2-10y=-38
%28x%5E2%2B6x%29%2B%28y%5E2-10y%29=-38...............complete squares
%28x%5E2%2B6x%2Bb%5E2%29+-b%5E2%2B%28y%5E2-10y%2Bb%5E2%29+-b%5E2+=-38
%28x%5E2%2B6x%2B3%5E2%29+-3%5E2%2B%28y%5E2-10y%2B5%5E2%29+-5%5E2+=-38
%28x%2B3%29%5E2+-9%2B%28y-5%29%5E2+-25+=-38
%28x%2B3%29%5E2+%2B%28y-5%29%5E2++=-38%2B34
%28x%2B3%29%5E2+%2B%28y-5%29%5E2++=+-4 -> negative number shows us it is not a circle
and the equation does+not match the form of any+conic section