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Math Help - Use the definition of a parabola and the distance

  1. #1
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    Use the definition of a parabola and the distance

    Hi all

    Use the definition of a parabola and the distance formula to find the equation of a parabola with

    a ) directix x = -4 and focus (2,2 )
    B ) directix x = 2 and focus (6,-4 )


    How i solve like this queation please hle me the steps to solve that

    thanks
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    For any point on parabola

    its distance from directrix and its distance from focus are equal

    So

    Distance of a point(h,k) from a line x= a

    is given by

    L= |{h-a}|


    Distance between two points (h,k) and (x,y) is given by

    D= \sqrt{(h-x)^2+(k-y)^2}

    D= L

    So |{h-a}| = \sqrt{(h-x)^2+(k-y)^2}

    You have been given all the values
    Solve it and ask if you still find it difficult.
    Last edited by ADARSH; April 20th 2010 at 02:45 AM.
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  3. #3
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    Quote Originally Posted by r-soy View Post
    Hi all

    Use the definition of a parabola and the distance formula to find the equation of a parabola with

    a ) directix x = -4 and focus (2,2 )
    B ) directix x = 2 and focus (6,-4 )


    How i solve like this queation please hle me the steps to solve that

    thanks


    Definition: a (plane) parabola is the locus of all points in the plane which are equidistant from a given line, called directrix, and a given fixed point called Focus.

    So , for example, in (a) you're looking for all the points (x,y)\in\mathbb{R}^2 s. t. their distances from the line x+4=0 and from the point (2,2) are the same, i.e.:

    \frac{|x+4|}{1}=\sqrt{(x-2)^2+(y-2)^2} ....well, now solve this equation (strongly recommended to square both sides) and find out the equation.

    Tonio
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  4. #4
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    I try to solve

    (x+4)^2 = ( X-2)^2 + (y-2) ^2

    x^2-16x+16=X^2-4x+4 + y2-4y+4

    x^2-16x+16-X^2+4x-4 -y2+4y-4
    12x-y^2-8 = 0

    I want check my answer
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  5. #5
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    Quote Originally Posted by r-soy View Post
    I try to solve

    (x+4)^2 = ( X-2)^2 + (y-2) ^2

    x^2-16x+16=X^2-4x+4 + y2-4y+4


    It must be +16x on the left side above, but basically it is correct.

    Toni



    x^2-16x+16-X^2+4x-4 -y2+4y-4
    12x-y^2-8 = 0

    I want check my answer
    .
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