#### JustRandomThings

##### Member

- Joined
- Jun 26, 2016

- Messages
- 59

- Gender
- Male

- HSC
- 2018

I need help with part 3 of this question

The ellipse E1 has equation x^2/a^2 + y^2/b^2=1 and ellipse E2 has equation x^2/b^2 + y^2/a^2=1. The point P(x0,y0) lies outside both E1 and E2.

i) Find all the points of intersection of E1 and E2

ii) The chord of contact of E1 from the point P(x0,y0) has equation xx0/a^2 + yy0/b^2 =1. This chord of contact intersects with the chord of contact to E2 from the point P(x0,y0) at the point Q(x2,y2). Find the coordinates of Q

iii) Using your answer to part (i) or otherwise show that Q cannot lie outside both E1 and E2