   Chapter 10.1, Problem 74E

Chapter
Section
Textbook Problem

Particle Motion Consider a particle traveling clockwise on the elliptical path x 2 100 + y 2 25 = 1. The particle leaves the orbit at the point (-8, 3) and travels in a straight line tangent to the ellipse. At what point will the particle cross the y-axis?

To determine

To calculate: The point where the straight line cuts the y-axis when a particle was travelling clockwise in the direction of the equation of an ellipse x2100+y225=1 and leaves the ellipse at the point (−8, 3).

Explanation

Given: A particle was travelling clockwise in the direction of the equation of an ellipse x2100+y225=1 and leaves the ellipse at the point (−8, 3).

Calculation:

The slope of the tangent to the conic is given by differentiating both sides w.r.t. x we have

x50+2y25dydx=0

dydx=

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