math

Find the standard form of the equation of the parabola with the given characteristics.
Vertex: (-9, 8); directrix: x = -16

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  1. plug and chug
    (y-k)^2 = 4a (x-h)
    k = 8 given
    h = -9 given
    distance from vertex to directrix = a
    distance from -9 to - 16 = 7 = a (positive for directrix to the left of the vertex)
    so
    (y-8)^2 = 28 (x+9)

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  2. Focus: ​(1515​,00​)​; ​ Directrix: xequals=negative 15

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  3. Focus: ​(15,0​)​; ​ Directrix: x= -15

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