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Math Help - equation of tangent question

  1. #1
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    equation of tangent question

    The straight line y = -x + 4 cuts the parabola with equation y = 16 - x^2 at the points A and B.

    a) Find the coordinates of A and B.


    Soo... since the line meets the parabola, I can solve by equating the equation of the line and the equation of the parabola/the equation of the gradient of the parabola. I ended up using the equation of the gradient.

    So:

    -x + 4 = -2x
    x= -4

    Subbing that into the equation of the parabola, I get y=0, so my first point is (-4, 0).

    What is the exact method to find a second point?
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  2. #2
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    I gave it a try by setting -x+4=16 - x^2
    and i get (4,0) and (-3, 7)
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  3. #3
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    Quote Originally Posted by shawli View Post
    The straight line y = -x + 4 cuts the parabola with equation y = 16 - x^2 at the points A and B.

    a) Find the coordinates of A and B.


    Soo... since the line meets the parabola, I can solve by equating the equation of the line and the equation of the parabola/the equation of the gradient of the parabola. I ended up using the equation of the gradient.
    No. This has nothing to do with the gradient, nor is this a tangent line. The line will cut the parabola when y= -x+ 4= 16- x^2. Solve that equation for x (two values since it is quadratic) and find the corresponding values of y.

    So:

    -x + 4 = -2x
    x= -4

    Subbing that into the equation of the parabola, I get y=0, so my first point is (-4, 0).

    What is the exact method to find a second point?
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