To show : the three normal from point
Explanation of Solution
Given information :
Curve
Formula needed :
Slope of tangent line is
Differentiate
So, the slope of normal is
As the normal line passes through points
Equate
So,
The two normal are perpendicular to each other if the product of their slopes is negative 1.
Consider two points on the curve are
As both points are symmetric to x-axis,
The product of slopes is
Thus, the points are
Equation of normal line passing through
The point
Third coordinate is
Chapter 3 Solutions
AP CALCULUS TEST PREP-WORKBOOK
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning