Tangent lines for a hyperbola Find an equation of the line

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567 2

Solution for problem 78E Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Problem 78E

Tangent lines for a hyperbola Find an equation of the line tangent to the hyperbola $x^2/a^2 - y^2/b^2 = 1$ at the point $(x_0, y_0)$.

Step-by-Step Solution:

Solution 78E
Step 1:

To find the tangent line at a point, first we need to find the slope( $\frac{dy}{dx}$ ) at the point.

Differentiating $\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1$ with respect to x to obtain $\frac{dy}{dx}$ , we get
$\frac{d}{dx}(\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}})=\frac{d}{dx}(1)$
$\frac{d}{dx}\frac{{x}^{2}}{{a}^{2}}-\frac{d}{dx}\frac{{y}^{2}}{{b}^{2}}=0$
$\frac{{2x}^{\ }}{{a}^{2}}-\frac{2y}{{b}^{2}}\frac{dy}{dx}=0$
$\frac{dy}{dx}=\frac{{b}^{2}x}{{a}^{2}{y}^{\ }}$

Using the above result, the slope(m) at point $\left({{x}_{0},{y}_{0}}\right)$ is $m=\frac{{b}^{2}{x}_{0}}{{a}^{2}{{y}_{0}}^{\ }}$

Step 2 of 2

Chapter 10.4, Problem 78E is Solved

Textbook: Calculus: Early Transcendentals

Edition: 1

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567

The answer to “?Tangent lines for a hyperbola Find an equation of the line tangent to the hyperbola $x^2/a^2 - y^2/b^2 = 1$ at the point $(x_0, y_0)$.” is broken down into a number of easy to follow steps, and 25 words. Since the solution to 78E from 10.4 chapter was answered, more than 352 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: hyperbola, Tangent, equation, Find, line. This expansive textbook survival guide covers 112 chapters, and 5248 solutions. The full step-by-step solution to problem: 78E from chapter: 10.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.