Explanation Given: L is the unique line that intersects the ellipse only n the one point P . Calculation: a. It is given that L is the unique line that intersects the ellipse only in the one point P that means the rest of the line will lie outside the ellipse. A point Q will be on the line but Q ≠ P . Q R will not be having the zero length and F 2 Q R will form a triangle. So, Q F 1 + Q F 2 = Q R + R F 1 + Q F 2 = R F 1 + ( Q R + Q F 2 ) = R F 1 + R F 2 Q F 1 + Q F 2 > R F 1 + R F 2 As the sum of the length of two sides of triangle exceeds the length of the third side...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 12.5, Problem 71E

To determine

a. That $Q F_{1} + Q F_{2} > P F_{1} + P F_{2}$ for all points Q on the tangent line other than P.

b. That $θ_{1} = θ_{_{2}}$ by using the Principle of Least Distance.

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Chapter 12.5, Problem 70E

Chapter 12.5, Problem 72E

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Chapter 12 Solutions

Calculus - Standalone book

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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a. That Q F 1 + Q F 2 > P F 1 + P F 2 for all points Q on the tangent line other than P . b. That θ 1 = θ 2 by using the Principle of Least Distance.

Solution Summary: The author explains the Principle of Least Distance, which states that the light will take the shortest path through P.

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a. That $Q F_{1} + Q F_{2} > P F_{1} + P F_{2}$ for all points Q on the tangent line other than P.

b. That $θ_{1} = θ_{_{2}}$ by using the Principle of Least Distance.

Want to see the full answer?

Chapter 12 Solutions

a. That Q F 1 + Q F 2 &gt; P F 1 + P F 2 for all points Q on the tangent line other than P . b. That θ 1 = θ 2 by using the Principle of Least Distance.

Solution Summary: The author explains the Principle of Least Distance, which states that the light will take the shortest path through P.

Videos

a. That QF1+QF2>PF1+PF2 for all points Q on the tangent line other than P. b. That θ1=θ2 by using the Principle of Least Distance.

Want to see the full answer?

Chapter 12 Solutions

a. That Q F 1 + Q F 2 > P F 1 + P F 2 for all points Q on the tangent line other than P . b. That θ 1 = θ 2 by using the Principle of Least Distance.

a. That $Q F_{1} + Q F_{2} > P F_{1} + P F_{2}$ for all points Q on the tangent line other than P.

b. That $θ_{1} = θ_{_{2}}$ by using the Principle of Least Distance.