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Math Help - parabola

  1. #1
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    parabola

    Questions:

    1) If a chord of the parabola y=4ax subtends a right angle at the vertex, show that the tangents at the extremeties meet on the line x+4a=0.
    2) A normal at point 't₁' of the parabola y=4ax cuts the parabola again at point 't₂' . Then prove that t₂∈(-∞,-2√(2 ])∪[2√2,∞).
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  2. #2
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    Quote Originally Posted by Pulock2009 View Post
    Questions:

    1) If a chord of the parabola y=4ax subtends a right angle at the vertex, show that the tangents at the extremeties meet on the line x+4a=0.
    ...
    1. The tangent point T lies on the positive branch of the parabola (y > 0) and the line y = x. Calculate T. (for confirmation only: T(4a, 4a)

    2. Calculate the slope of tangent using implicite differentiation. (for confirmation only: y'=\frac{2a}{2\sqrt{ax}} )

    3. Calculate the equation of the tangent in T. (for confirmation only: y = \frac12 x +2a )

    4. According to the method shown for the first tangent determine the equation of the second tangent. (for confirmation only: y = -\frac12 x -2a )

    5. Determine the point of intersection between the two tangents and show that it satisfies the given equation.
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