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 = _____.

Question

Aicharya · Accepted Answer

Plotting the diagram as per given data we get,

$P_1$: Directrix $x + 2y = k$ $x + 2y - k = 0$ $\left| \frac{3 + 4 - K}{\sqrt{5}} \right| = \sqrt{5}$ $\left| 7 - k \right| = 5$ $\begin{aligned} 7 - K &= 5, & 7 - K &= -5, \\ k &= 2, & k &= 12, \\ \text{Accepted}, & \text{Rejected Passes through focus} \end{aligned}$ $D_1 = x + 2y = 2$ $= x + 2y = 6$ $D_2 = x + 2y = C \Rightarrow d \Rightarrow d \Rightarrow c = 10$

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…

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