Show, using the focus-directrix property for an ellipse, that PS +PS'=2a where P is a point on the ellipse and S and S' are the two foci.

The focus diretrix property for an ellipse is PS/PD=e. Now this is also the case for the other directrix and focus, so PS'/PD'=e. Now we can rearrange these equations to find a formula for PS +PS', PS +PS'=e(PD+PD'). Using a simple diagram we can see PD+PD'= 2ae by marking on some distances. Subbing into the above equation yields PS +PS'=2a. 

DL
Answered by Daniel L. Further Mathematics tutor

10232 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.


(FP1) Given k = q + 3i and z = w^2 - 8w* - 18q^2 i, and if w is purely imaginary, show that there is only one possible non-zero value of z


Find the eigenvalues and eigenvectors of A = ([2, 0 , 0], [0, 1, 1], [0, 3, 3])


How to calculate the integral of sec(x)?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning