Q59 / 90 · JEE Main 2022 (24 Jun Shift 2) · Mathematics

Let $P_{1}$ be a parabola with vertex $(3, 2)$ and focus $(4, 4)$ and $P_{2}$ be its mirror image with respect to the line $x + 2 y = 6$ . Then the directrix of $P_{2}$ is $x + 2 y =$ _____.

Correct answer: 10

Solution

Plotting the diagram as per given data we get,

$P_{1}$ : Directrix

$x + 2 y = k$

$x + 2 y - k = 0$

$|\frac{3 + 4 - K}{\sqrt{5}}| = \sqrt{5}$

$|7 - k| = 5$

$\begin{matrix} 7 - K = 5 & 7 - K = - 5 \\ k = 2 & k = 12 \\ Accepted & Rejected Passes through focus \end{matrix}$

$\begin{array}{l} D_{1} = x + 2 y = 2 \\ = x + 2 y = 6 \\ D_{2} = x + 2 y = C \end{array}] \Rightarrow d \Rightarrow d \Rightarrow c = 10$

Hence, the correct answer is 10.