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

TestHub · Accepted Answer

Plotting the diagram as per given data we get,

$P_{1}$ : Directrix

$x + 2 y = k$

$x + 2 y - k = 0$

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

$|7 - k| = 5$

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

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

Mathematics - Parabola Question with Solution | TestHub

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