Question 1085731


{{{x^2+y^2+6x−10y+38=0 }}}...to check if it is a circle, write the equation in form {{{(x-h)^2+(y-k)^2=r^2}}}

{{{x^2+6x+y^2-10y=-38}}}

{{{(x^2+6x)+(y^2-10y)=-38}}}...............complete squares

{{{(x^2+6x+b^2) -b^2+(y^2-10y+b^2) -b^2 =-38}}}

{{{(x^2+6x+3^2) -3^2+(y^2-10y+5^2) -5^2 =-38}}}

{{{(x+3)^2 -9+(y-5)^2 -25 =-38}}}

{{{(x+3)^2 +(y-5)^2  =-38+34}}}

{{{(x+3)^2 +(y-5)^2  = -4}}} -> negative number shows us it is {{{not}}} a circle

and the equation {{{does}}}{{{ not}}} match the form of {{{any}}}{{{ conic}}} section