Complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle. Please show work or an explanation with the solution.

 

x^2+y^2+ 5x−y−1 = 0

Center,(h,k)=(−25?,21?)?

?Radius,a=215???

Step-by-step explanation

?x2+y2+5x−y−1=0?

?x2+5x+y2−y−1=0?

In order to make ?x2+5x? into a perfect square add ?(25?)2? so that it will become ?x2+5x+(25?)2=? ?(x+25?)2?

In order to make ?y2−y? into a perfect square add ?(21?)2? so that it will become ?y2−y+(21?)2=(y−21?)2?

So,

?x2+5x+(25?)2+y2−y+(21?)2−1=0+(25?)2+(21?)2?

?x2+5x+(25?)2+y2−y+(21?)2=(25?)2+(21?)2+1?

?(x+25?)2+(y−21?)2=(25?)2+(21?)2+1?

?(x+25?)2+(y−21?)2=215??

?(x+25?)2+(y−21?)2=(215??)2?

This is the standard form.

Comparing this equation with ?(x−h)2+(y−k)2=a2? we have,

?Center,(h,k)=(−25?,21?)?

?Radius,a=215???