conics Q (1 Viewer)

[jkwii]

got a Q

let the lengths of the perpendiculars from the foci of an ellipse 4x^2 + 9y^2 = 36 be P1 and P2. prove that P1xP2 = 4. Also prove that the points of contacts lie on the auxilary circle x^2 + y^2 = 9

 

[samwell]

4x^2 + 9y^2 = 36
x^2/9 + y^2/ 4 =1
b^2= a^2(1- e^2)
4=9(1- e^2)
e= sq root 5 /3
foci( +/- ae, 0)
(+/- sq root 5, O)
P1= 5/9 + y^2/4 =1
y^2 =16/9
y=4/3
P1 x P2= 16/9
it doesnt come to 4 it comes to 16/9

 

[jkwii]

yes p1 x p2 = 4 its the same proof as prove that p1 x p2 = b^2... i just wanted to know about showing that the points of intersections between lines p1 and p2 and the tangent lie on the circle x^2 + y^2 = 9...