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    The 2 points on the curve x^2 + y^2 - xy = 84 where the gradient of the curve is 1/3 are A and B. Find the eqns of the tangents at A and B.

    my method was:

    1) differentiate
    2) sub 1/3 into dy/dx found in the implicit eqn.
    3) use this to find the value of x and y
    4) then finding the tangent for these values

    Not getting the right answer? Any idea why?
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    (Original post by A*my)
    The 2 points on the curve x^2 + y^2 - xy = 84 where the gradient of the curve is 1/3 are A and B. Find the eqns of the tangents at A and B.

    my method was:

    1) differentiate
    2) sub 1/3 into dy/dx found in the implicit eqn.
    3) use this to find the value of x and y
    4) then finding the tangent for these values

    Not getting the right answer? Any idea why?
    2) Give a relationship between x and y, 5x=y.

    Subbing back into the orginal equation gives two possible values for x, +/-2.

    Sub each into original gives 4 possible points.

    Check each for correct gradient, leaves (2,10), and (-2,-10).

    Then work out tangents.

    Probably an arithmetic slip on your part assuming the given answer is correct.
 
 
 
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Updated: November 11, 2017

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