JEE PYQ: Parabola Question 8
Question 8 - 2020 (05 Sep Shift 1)
If the common tangent to the parabolas, $y^2 = 4x$ and $x^2 = 4y$ also touches the circle, $x^2 + y^2 = c^2$, then $c$ is equal to:
(1) $\frac{1}{2\sqrt{2}}$
(2) $\frac{1}{\sqrt{2}}$
(3) $\frac{1}{4}$
(4) $\frac{1}{2}$
Show Answer
Answer: (2)
Solution
Tangent to $y^2 = 4x$: $y = mx + \frac{1}{m}$. Tangent to $x^2 = 4y$: $y = mx - m^2$. So $\frac{1}{m} = -m^2 \Rightarrow m = -1$. Common tangent: $x + y + 1 = 0$. Distance from origin $= \frac{1}{\sqrt{2}} = c$.
BETA
