Explanation Given: The perpendicular distances F 1 R 1 and F 2 R 2 Calculation: The standard equation of an ellipse will be given by: ( x a ) 2 + ( y b ) 2 = 1 ... ( 1 ) Equation of the tangent to this ellipse at the point ( x 0 , y 0 ) will be given by: ( x x 0 a ) 2 + ( y y 0 b ) 2 = 1 ... ( 2 ) Now, simplify the equation (2) and we get: ( x x 0 a ) 2 + ( y y 0 b ) 2 = 1 b 2 x 2 x 0 2 + a 2 y 2 y 0 2 − a 2 b 2 = 0 ... ( 3 ) So, the length of perpendiculars on this tangent from the two foci is given by: F 1 R 1 = b 2 x 0 ( − c ) − a 2 b 2 b 4 x 0 2 + a 4 y 0 2 F 2 R 2 = b 2 x 0 ( c ) − a 2 b 2 b 4 x 0 2 + a 4 y 0 2 Now, multiply these perpendicular distances and we get: F 1 R 1 × F 2 R 2 = b 2 x 0 ( − c ) − a 2 b 2 b 4 x 0 2 + a 4 y 0 2 × b 2 x 0 ( c ) − a 2 b 2 b 4 x 0 2 + a 4 y 0 2 F 1 R 1 × F 2 R 2 = b 4 ( a 4 − c 2 x 0 2 ) b 4 x 0 2 + a 4 y 0 2 .....

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Videos

Question

Chapter 12, Problem 55CRE

To determine

That the product of the perpendicular distances $F_{1} R_{1}$ and $F_{2} R_{2}$ from the foci to a tangent line of an ellipse is equal to the square $b^{2}$ of the semi minor axes

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12, Problem 54CRE

Chapter 13.1, Problem 1PQ

Students have asked these similar questions

Q6. A fossil piece has been found in Alberta that contains 34% of C14 in it. What is the age of this fossil piece?

Q5. Briefly explain what are isotopes of an elements, with an example, and why some isotopes are radioactive. 470

Q1. Will you earn more interest amount in two years by depositing $2000 in a simple interest account that pays 6% or in an account that pays 6.15% interest compounded monthly? t

Chapter 12 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

That the product of the perpendicular distances F 1 R 1 and F 2 R 2 from the foci to a tangent line of an ellipse is equal to the square b 2 of the semi minor axes

Solution Summary: The author proves that the product of the perpendicular distances F 1 R 1 and F 2 R 2 from the foci to a tangent line of an ellipse is equal to the square b

Videos

That the product of the perpendicular distances $F_{1} R_{1}$ and $F_{2} R_{2}$ from the foci to a tangent line of an ellipse is equal to the square $b^{2}$ of the semi minor axes

Want to see the full answer?

Chapter 12 Solutions

That the product of the perpendicular distances F 1 R 1 and F 2 R 2 from the foci to a tangent line of an ellipse is equal to the square b 2 of the semi minor axes

Solution Summary: The author proves that the product of the perpendicular distances F 1 R 1 and F 2 R 2 from the foci to a tangent line of an ellipse is equal to the square b

Videos

That the product of the perpendicular distances F1R1 and F2R2 from the foci to a tangent line of an ellipse is equal to the square b2 of the semi minor axes

Want to see the full answer?

Chapter 12 Solutions

That the product of the perpendicular distances $F_{1} R_{1}$ and $F_{2} R_{2}$ from the foci to a tangent line of an ellipse is equal to the square $b^{2}$ of the semi minor axes