Finding Equations of Tangent Lines and Normal Lines In Exercises 49 and 50, find equations fur (a) the tangent lines and (b) the normal lines to the hyperbola for the given value of x. (The normal line at a point is perpendicular to the tangent line at the point.)
To-calculate: The of the tangent lines for the hyperbola at .
The equation of the hyperbola, and .
Equation of a line passes through and slope is .
Consider the provided equation of the hyperbola, .
Now, substitute in the equation of the hyperbola, , to find the coordinate for .
Thus, the two coordinates are and .
Now, differentiate the equation of the hyperbola, with respect to .
Since, is the slope of the curve at any point on the curve of the hyperbola,
So, the slope of the hyperbola, at is,
Now, with the help of the standard equation of the line , calculate the equation of the tangent passing through and with a slope of
To-calculate: The equations of the normal lines for the hyperbola at .
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Calculus: Early Transcendental Functions
Calculus: An Applied Approach (MindTap Course List)
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals, Volume I
Precalculus: Mathematics for Calculus (Standalone Book)
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Essentials Of Statistics
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus (MindTap Course List)
Understanding Basic Statistics
Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus
Probability and Statistics for Engineering and the Sciences
Mathematical Excursions (MindTap Course List)
Mathematical Applications for the Management, Life, and Social Sciences
Single Variable Calculus: Early Transcendentals
Contemporary Mathematics for Business & Consumers
Elementary Geometry For College Students, 7e
Trigonometry (MindTap Course List)
Elements Of Modern Algebra
Elementary Technical Mathematics
Calculus of a Single Variable
Calculus: Early Transcendental Functions (MindTap Course List)
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students