Question:
If the common tangent to the parabolas, $y^{2}=4 x$ and $x^{2}=4 y$ also touches the circle, $x^{2}+y^{2}=c^{2}$, then $c$ is equal to :
Correct Option: , 3
Solution:
$y=m x+\frac{1}{m}\left(\operatorname{tangent}\right.$ at $\left.y^{2}=4 x\right)$
$y=m x-m^{2}\left(\operatorname{tangent}\right.$ at $\left.x^{2}=4 y\right)$
$\frac{1}{m}=-m^{2}$ (for common tangent)
$m^{3}=-1$
$\mathrm{m}=-1$
$y=-x-1$
$x+y+1=0$
This line touches circle
$\therefore$ apply $\mathrm{p}=\mathrm{r}$
$c=\left|\frac{0+0+1}{\sqrt{2}}\right|=\frac{1}{\sqrt{2}}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.