Center of Curvature Let C be a curve given by .
Let K be the curvature at the point and let
Show that the coordinates of the center of curvature at P are ( .
To prove: The co-ordinates of the center of curvature at P are .
The curve C is given by , K is the curvature at point and .
Is the point on curve .
Let be the center of curvature.
The radius of curvature is .
So, slope of normal line at is .
Equation of normal line,
Since, is on normal line.
And, lies on the circle.
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Calculus: Early Transcendentals
Finite Mathematics and Applied Calculus (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: An Applied Approach (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus: Early Transcendental Functions
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Understanding Basic Statistics
Single Variable Calculus
Mathematical Applications for the Management, Life, and Social Sciences
Mathematical Excursions (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Single Variable Calculus: Early Transcendentals
Elements Of Modern Algebra
Contemporary Mathematics for Business & Consumers
Trigonometry (MindTap Course List)
Elementary Technical Mathematics
Elementary Geometry For College Students, 7e
Calculus: Early Transcendental Functions (MindTap Course List)
Calculus of a Single Variable
Finite Mathematics for the Managerial, Life, and Social Sciences
Elementary Geometry for College Students