Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 years ago

Geometry question - parabola! (giving points to best answer)?

A parabola has a focus of F(1,3) and a directrix of y=2.

P(x,y) represents any point on the parabola, while D(x,2) represents any point on the directrix.

What are the steps required to find the equation of the parabola?

1 Answer

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  • Pope
    Lv 7
    3 years ago
    Favorite Answer

    Notice that PD is the distance from P to the directrix. The parabola is the locus of all points equidistant from the focus and the directrix.

    PF = PD

    √[(x - 1)² + (y - 3)²] = |y - 2|

    (x - 1)² + (y - 3)² = (y - 2)²

    x² - 2x + 1 + y² - 6y + 9 = y² - 4y + 4

    x² - 2x - 2y + 6 = 0

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