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Mirror image of a parabola in a line

This type of question, asked 3 times: 14 Jun 2022, 28 Jan 2025, 24 Jan 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    14 Jun 2022

    180
    Let P1P_{1} be a parabola with vertex (3,2)\left( 3,2 \right) and focus (4,4)\left( 4,4 \right) and P2P_{2} be its mirror image with respect to the line x+2y=6x+ 2y= 6. Then the directrix of P2P_{2} is x+2y=x+ 2y=

  2. Question 2

    28 Jan 2025

    149
    Let AA and BB be the two points of intersection of the line y+5=0y + 5 = 0 and the mirror image of the parabola y2=4xy^{2}= 4x with respect to the line x+y+4=0x + y + 4 = 0. If dd denotes the distance between AA and BB, and a denotes the area of △SAB\bigtriangleup SAB, where SS is the focus of the parabola y2=4xy^{2}= 4x, then the value of (a+d)(a + d) is ______\_\_\_\_\_\_ .

  3. Question 3

    24 Jan 2026 S2

    56
    Let the image of parabola x2=4yx^{2}= 4y, in the line x−y=1x - y = 1 be (y+α)2=b(x−c),a,b,c∈N(y + \alpha)^{2}= b(x - c),a,b,c \in N. Then a+ba + b +c is equal to

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