Question

Find the equation of k for which the equation $x^2+y^2+4x-2y-k=0$ represents a point circle

• A. $5$
• B. $-5$
• C. $6$
• D. $-6$
• E. none of these

Answer 1

The correct option is B $-5$

Standard form of circle is

$(x-x_1{)}^2+(y-y_1{)}^2=r^2$

When $(x_1,y_1)$ is the centre of the circle and $r$ is the radius of the circle.

Now,given equation is,

$x^2+y^2+4x-2y-k=0$

$=>x^2+4x+y^2-2y=k$

$=>x^2+2.x.2+2^2+y^2-2.y.1+1^1=k+2^2+1^1$

$=>(x+2{)}^2+(y-1{)}^2=k+4+1$

$=>(x+2{)}^2+(y-1{)}^2=k+5$

Since it represents a point circle

$\therefore k+5=0$

$=>k=-5$