To show: The tangent line to the ellipse at the point
Explanation of Solution
Given:
The equation of ellipse is
The equation of ellipse at
Derivative rule: Chain rule
If
Formula used:
The equation of the tangent line at
Where, m is the slope of the tangent line at
Proof:
Obtain the equation of tangent line to the ellipse at
Consider the equation of ellipse
Differentiate implicitly with respect to x,
Apply the chain rule (1) and simplify the terms,
Multiply the equation by
Thus, the derivative of the equation is
The slope of the tangent line at
Substitute
Therefore, the slope of the tangent at
Substitute
Divided the equation by
Substitute
Hence, it can be concluded that the tangent line to the ellipse at the point
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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