Chapter 2.P, Problem 22P

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Given an ellipse

To determine

**To find:** The equation of the set of all points from which there are two tangents to the curve whose slopes are,

(a) Reciprocals

(b) Negative reciprocals

Explanation

**1) Formula:**

i. Point-slope formula:

ii.

iii. Discriminant =

iv. Quadratic formula:

v. If

**2) Given:**

Equation of ellipse is,

3) **Calculation:**

By using point-slope formula the equation of tangent which pass through the point (c, d) is,

To find the point where it touches the ellipse, substitute in equation of ellipse,

By solving it,

By using formula ii,

Again by using formula ii,

By solving it,

Now, discriminant of this equation must be zero since a tangent line touches a curve at only one point

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