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Math Help - Sums of x and y intercerpts of any tangent line to the curve

  1. #1
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    Sums of x and y intercerpts of any tangent line to the curve

    can anyone help me with this question?

    Prove that the sum of the x and y intercepts of any tangent line to the curve x^1/2 + y^1/2 = k^1/2 is constant and is equal to k.
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  2. #2
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    Quote Originally Posted by rawrzjaja View Post
    can anyone help me with this question?

    Prove that the sum of the x and y intercepts of any tangent line to the curve x^1/2 + y^1/2 = k^1/2 is constant and is equal to k.
    First get the equation of the tangent at to the curve at x = a. Can you do that?
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    First get the equation of the tangent at to the curve at x = a. Can you do that?
    Once you do this, solve for both the x and y intercepts. Add them together. They should be equal to k.
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    not too sure how to get x = a... sry T_T, can you show me please
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  5. #5
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    Quote Originally Posted by rawrzjaja View Post
    not too sure how to get x = a... sry T_T, can you show me please
    In more detail: What I've suggested is find the tangent at the general point (a, b) where b is related to a via the equation for the curve.
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