   Chapter 10.1, Problem 67E

Chapter
Section
Textbook Problem

# Proof(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 x 2 − 4 x − 4 y = 0 at the points (0.0) and (6.3).

63)

(a)

To determine

To Prove: Two distinct tangent lines to a parabola intersect at a point.

Explanation

Given: the parabola y=x2

Proof: Consider the equation of parabola, y=x2.

The slope of the tangent is provided by dydx=2x.

Consider the two points a and b,

Thus, the equation of the tangent lines at a and b are given by,

ya2=2a(xa) and yb2=2a(xb)

Solve the equations for x,

2a(xa)+a2=2b

(b)

To determine

To Calculate: The points of intersection of tangent lines to the parabola x24x4y=0 with the help of explanation in part (a) at the two given points(0, 0) and (6, 3).

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