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Parabola from its vertex or focus and its directrix or tangent at the vertex

This type of question, asked 5 times: 27 Jun 2022, 28 Jun 2022, 27 Jul 2022, 24 Jan 2025, 7 Apr 2025. All 5 questions below, oldest first.

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  1. Question 1

    27 Jun 2022

    161
    If the equation of the parabola, whose vertex is at (5,4)(5,4) and the directrix is 3x+y−29=03x + y - 29 = 0, is x2+ay2+bxy+cx+dy+k=0x^{2}+ ay^{2}+ bxy + cx + dy + k = 0 then a+b+c+d+ka + b + c + d + k is equal to

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  2. Question 2

    28 Jun 2022

    165
    If vertex of a parabola is (2,−1)(2, - 1) and the equation of its directrix is 4x−3y=214x - 3y = 21, then the length of its latus rectum is

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  3. Question 3

    27 Jul 2022

    163
    If the length of the latus rectum of a parabola, whose focus is (a,a)(a,a) and the tangent at its vertex is x+y=ax + y = a, is 16, then ∣a∣|a| is equal to :

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  4. Question 4

    24 Jan 2025

    145
    If the equation of the parabola with vertex V(32,3)V\left( \frac{3}{2},3 \right) and the directrix x+2y=0x + 2y = 0 is αx2+βy2−γxy−30x−60y+225=0\alpha x^{2}+ \beta y^{2}- \gamma xy - 30x - 60y + 225 = 0, then α+β+γ\alpha + \beta + \gamma is equal to:

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  5. Question 5

    7 Apr 2025

    55
    Let PP be the parabola, whose focus is (−2,1)\left( - 2,1 \right) and directrix is 2x+y+2x+y+ 2=02 = 0. Then the sum of the ordinates of the points on P , whose abscissa is -2 , is.

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