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Math Help - Coordinate systems

  1. #1
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    Coordinate systems

    Find, in cartesian form, an equation of the parabola whose focus and directrix are respectively (3, 0), x+5 = 0.

    How can I find?


    As I know y^2 = 4ax is a cartesian equation of the parabola. And every point on the parabola is equidistant from the focus (a, 0) and the directrix x+a = 0.

    But here, there are 2 different values of a.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by geton View Post
    Find, in cartesian form, an equation of the parabola whose focus and directrix are respectively (3, 0), x+5 = 0.

    How can I find?


    As I know y^2 = 4ax is a cartesian equation of the parabola. And every point on the parabola is equidistant from the focus (a, 0) and the directrix x+a = 0.

    But here, there are 2 different values of a.
    y^2 = 4ax represents a parabola that opens either to the right or left. Yours opens to the right, so a is positive. The perpendicular line between the focus and the directrix is bisected by the vertex, so your vertex is at (-1, 0). Does this help?

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    y^2 = 4ax represents a parabola that opens either to the right or left. Yours opens to the right, so a is positive. The perpendicular line between the focus and the directrix is bisected by the vertex, so your vertex is at (-1, 0). Does this help?

    -Dan
    Yes I got it. a's value is 4 actually. And by substitution, I got y^2 = 16x + 16.

    Thank you.
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