   Chapter 10, Problem 9RQ

Chapter
Section
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.9. A tangent line to a parabola intersects the parabola only once

To determine

To find: Whether the given statement is true or false and explain with an example if necessary to prove your answer.

Explanation

Given:

The standard equation of parabola is as follows.

y=cx2 (1)

Where c >0

Calculation:

Substitute a for x in equation (1)

y=ca2

Consider the tangent line yca2=2ca(xa) at point (a,ca2) .

yca2=2ca(xa)

yca2=2cax2ca2

y=2caxca2 (2)

Consider the tangent line meet the parabola at (x,cx

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