equation for a parabola with a focus of (2, -2) and a directrix of y=-8

Question

equation for a parabola with a focus of (2, -2) and a directrix of y=-8

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Aubrey 3 weeks 2021-10-04T01:11:24+00:00 2 Answers 0

Answers ( )

    0
    2021-10-04T01:12:52+00:00

    Answer:

    y=1/8(-x^2+4x+44

    Step-by-step explanation:

    In this question the given focus is (2,4) and a directrix of y = 8 and we have to derive the equation of the parabola.

    Let (x,y) is a point on the given parabola.Then the distance between the point (x,y) to (2,4) and the distance from (x,y) to diractrix will be same.

    Distance between (x,y) and (2,4)

    = √(x-2)²+(y-4)²

    And the distance between (x,y) and directrix y=8

    = (y-8)

    Now √(x-2)²+(y-4)² = (y-8)

    (x-2)²+(y-4)² = (y-8)²

    x²+4-4x+y²+16-8y = y²+64-16y

    x²+20+y²-4x-8y = y²-16y+64

    x²+20-4x-8y+16y-64=0

    x²+8y-4x-44 = 0

    8y = -x²+4x+44

    0
    2021-10-04T01:12:59+00:00

    Y=1/8(x^2+4x+44) is correct

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45:7+7-4:2-5:5*4+35:2 =? ( )