Question

If the curves $\frac{x^2}{4}+y^2=1$ and $\frac{x^2}{a^2}+y^2=1$ cut on four concylic points for some suitable value of ' $a$ ' then equation of circle passing through these four points, is

• A. $x^2+y^2=1$
• B. $x^2+y^2=2$
• C. $x^2+y^2=4$
• D. None of these

Answer 1

Answer: (A)

Let equation of circle be $\left(\frac{x^2}{4}+y^2-1\right)+\lambda\left(\frac{x^2}{a^2}+y^2-1\right)=0$
$\Rightarrow x^2\left(\frac{1}{4}+\frac{\lambda}{a^2}\right)+y^2(1+\lambda)=(1+\lambda) $
$\Rightarrow x^2\left(\frac{a^2+4 \lambda}{4 a^2(1+\lambda)}\right)+y^2=1$