(a) Prove that any two distinct tangent lines to a parabola interact.
(b) Demonstrate the result of part (a) by finding the point intersection of the tangent lines to the parabola
at the points (0.0) and (6.3).
To Prove: Two distinct tangent lines to a parabola intersect at a point.
Given: the parabola
Proof: Consider the equation of parabola, .
The slope of the tangent is provided by .
Consider the two points a and b,
Thus, the equation of the tangent lines at a and b are given by,
Solve the equations for x,
To Calculate: The points of intersection of tangent lines to the parabola with the help of explanation in part (a) at the two given points(0, 0) and (6, 3).
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