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dix123

  • one year ago

Can someone help me write an equation for a parabola using a focus and directrix? Medal and follow.

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  1. dix123
    • one year ago
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    someone plssssss help

  2. welshfella
    • one year ago
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    http://hotmath.com/hotmath_help/topics/finding-the-equation-of-a-parabola-given-focus-and-directrix.html this should help

  3. dix123
    • one year ago
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    thanks

  4. welshfella
    • one year ago
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    yw a simple one worth remembering is the parabola y^2 = 4ax where the focus is at (a,0) and directrix is x = -a

  5. welshfella
    • one year ago
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    |dw:1436266138651:dw|

  6. welshfella
    • one year ago
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    derivation: P is the point (x,y) the lines marked with 2 lines are equal (definition of a parabola) so a + x = sqrt (y^2 + (x -a)^2) (a + x)^2 = y^2 + x^2 - 2ax + a^2 a^2 + x^2 + 2ax = y^2 + x^2 - 2ax + a^2 which reduces to y^2 = 4ax

  7. welshfella
    • one year ago
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    |dw:1436266598022:dw|

  8. welshfella
    • one year ago
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    so if you need the equation of a parabola given focus = (2,0) and directrix x = -2 we can write ir straight away a = 2 y^2 = 4(2)x y^2 = 8x

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