(a)
To show : the tangent to the ellipse at point
(a)
Explanation of Solution
Given information :
The equation of ellipse is
Formula needed :
Power rule of derivative:
Product rule of derivative:
Differentiate
Solve further,
Substitute
The tangent line to ellipse at point
Simply the equation.
The point
So,
Hence proved, the tangent to the ellipse at point
(b)
To find : the tangent to the hyperbola at point
(b)
Answer to Problem 65E
Hence, the tangent to the hyperbola at point
Explanation of Solution
Given information :
The equation of hyperbola is
Formula needed :
Power rule of derivative:
Product rule of derivative:
Differentiate
Solve further,
Substitute
The tangent line to hyperbola at point
Simply the equation.
The point
So,
Hence, the tangent to the hyperbola at point
Chapter 3 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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