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Math Help - Find the Lines that are tangent and normal to curve at given point.

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    Junior Member Cyberman86's Avatar
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    Question Find the Lines that are tangent and normal to curve at given point.

    Find the Lines that are Tangent and Normal to the Curve at the given points.


    x^2+xy-y^2 = 11 , (3,1)


    a) Give the equation that is tangent to the curve.
    2x+(x dy/x + y dy/x) - 2y dy/dx = 0
    (x-2y)dy/dx + 2x+y = 0
    (x-2y)dy/dx = -2x-y
    dy/dx = -2x-y/x-2y

    dy/dx= -2(3)-1 / 3-2(1) = 7/1

    y= y1 + m(x-x1)
    y= 1 + 7/1(x-3) = ??? (I have tried many problems like this in Mymathlab and always get wrong this part)


    b) Give the Equation that is Normal to the Curve.

    y=1-7/1(x-3)

    y= (also can't get this part right)


    Please if Someone can show step by step how to do this problem I will appreciated.
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    Quote Originally Posted by Cyberman86 View Post
    Find the Lines that are Tangent and Normal to the Curve at the given points.


    x^2+xy-y^2 = 11 , (3,1)
    If m\ne 0 is the slope of the curve at (p,q) on the curve:
    The tangent is y-q=m(x-p) and the normal is y-q=\frac{-1}{m}(x-p).
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