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Equation of a parabola from its vertex and directrix

The same question, asked 2 times: 27 Jun 2022*, 24 Jan 2025. Every wording 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

    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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