To find: The equation of the both tangent lines to the ellipse passing through the point.
Answer to Problem 52E
The equation of the tangent line to the curve passing through the point
Explanation of Solution
Given:
The equation of the ellipse
The point is
Derivative rules:
Chain rule:
Calculation:
Obtain the slope of tangent to the equation.
Differentiate
Apply the chain rule and simplify the terms.
Thus, the derivative of the equation of the ellipse is
That is, the slope of the tangent is
Let
The slope of tangent to the curve at
The equation of the tangent line passing through the point
Here, the tangent line is also passing through the point
Substitute
The value of the curve
Substitute the equation (3) in equation (2).
Substitute
Simplify the quadratic equation,
Substitute
Thus, the value of b is 3.
Substitute
Thus, the points are
Substitute
Thus, the equation of the tangent line to the curve passing through the point
Substitute
Thus, the equation of the tangent line to the curve passing through the point
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning