Question

For what value of $k$, does the equation$9x^2+y^2=k\left(x^2-y^2-2x\right)$represent equation of a circle?

• A. 1
• B. 2
• C. -1
• D. 4

Answer 1

Answer: (D)

The given equation $9x^2+y^2=k\left(x^2-y^2-2x\right)$ can be written as
$9x^2+y^2-k{x}^2+k{y}^2+2kx=0$
$\Rightarrow (9-k)x^2+(1+k)y^2+2kx=0$
This equation represents a circle, if coefficients of $x^2$ and $y^2$ are equal.
so, $9-k=1+k$
$\Rightarrow 2k=8$
$\Rightarrow k=4$