Thread: parabola

Questions:

1) If a chord of the parabola y²=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 y²=4ax cuts the parabola again at point 't₂' . Then prove that t₂∈(-∞,-2√(2 ])∪[2√2,∞).

Originally Posted by Pulock2009

Questions:

1) If a chord of the parabola y²=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: )

3. Calculate the equation of the tangent in T. (for confirmation only: )

4. According to the method shown for the first tangent determine the equation of the second tangent. (for confirmation only: )

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