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Math Help - Implicit equation issue..

  1. #1
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    Implicit equation issue..

    4. Differentiate the implicit equation of the hyperbola 4x^2 - 3y^2 = 24 to find the equation of the normal at the point (3, -2). Find the y-coordinate of the point where the normal meets the curve again.

    Differentiating:

    => 8x - 6y dy/dx = 0
    => 8x = 6y dy/dx
    => dy/dx = 8x / 6y

    At (3, -2), the gradient of normal is 1 / m, where gradient = 24 / -12 = -2 :
    m = 1/2

    So the equation of the normal is:
    y + 2 = 1/2(x - 3)
    y = 1/2x - 3/2 - 2
    2y = x - 4

    I don't know where to go from here. How to find the y-coordinate of the point where the normal meets the curve again?
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  2. #2
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    Hi struck
    Quote Originally Posted by struck View Post
    y = 1/2x - 3/2 - 2
    2y = x - 4
    I think you want to check this once again ^^


    To find the point where the normal meets the curve again, subs. the equation of the normal to the equation of the curve.
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  3. #3
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    Quote Originally Posted by songoku View Post
    Hi struck


    I think you want to check this once again ^^


    To find the point where the normal meets the curve again, subs. the equation of the normal to the equation of the curve.
    Oh yea, it should be 2y = x - 7... But I still don't understand how to solve the next part. How do you sub. the equation of the normal to the equation of the curve
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  4. #4
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    Hi struck

    Equation of the curve : 4x^2 - 3y^2 = 24
    Equation of normal : 2y = x - 7 ---------------> x = 2y + 7

    Because the curve and the normal intersect :
    4x^2 - 3y^2 = 24
    4 (2y+7)^2 - 3y^2 = 24 --------> solve for y
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