Question

If the line $ax+y=c$, touches both the curves $x^2+y^2=1$ and $y^2=4\sqrt{2}x$, then $\left|c\right|$ is equal to:

• A. $1/2$
• B. $2$
• C. $\sqrt{2}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (C)

$\sqrt{2}$

Tangent to $y^2=4\sqrt{2}x$ is $y=mx+\frac{\sqrt{2}}{m}$ is also tangent to $x^2+y^2=1$

$\Rightarrow \left|\frac{\sqrt{2}/m}{\sqrt{1+m^2}}\right|=1\Rightarrow m=\pm 1$

Tangent will be $y=x+\sqrt{2}$ or $y=-x-\sqrt{2}$

compare with $y=-ax+c$

$\Rightarrow a=\pm 1;c=\pm \sqrt{2}$

$\therefore |c|=\sqrt{2}$