0

Guest

Courses New

Show that the double ordinate of the auxilliary circle of an ellipse passing through the focus is equal to the minor axis of the ellipse.

Show that the double ordinate of the auxilliary circle of an ellipse passing through the focus is equal to the minor axis of the ellipse.

Grade:11

1 Answers

Rajat
213 Points
5 years ago
Let the focus of the ellipse be F, the major axis be 'a' and minor axis be 'b'. Let PFP' be the double ordinate of the auxiliary circle where P and P' are points on the circle. let O be the origin then, OF = ae= sqrt(a^2-b^2).
triangle OFP is right angled. Thus OP^2-OF^2=PF^2
or, PF^2 = a^2-(a^2-b^2)= b^2
so, PF = b, therefore PFP' = 2b = minor axis

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More