Conics (1 Viewer)

[scardizzle]

P is a variable point on the ellipse with equation x^2/a + y^2/b = 1 and S and S' are the foci. Show that PS and PS' are equally inclined to the tangent at P.

 

[nrlwinner]

Use the angle bisector theorm

 

[ninetypercent]

soz but its hard to explain over the net

 

[Affinity]

given point P
1. find gradient of tangent at P
2. Find gradient of PS
3. Find gradient of PS'
4. use the result relating the tangent of the angle between 2 lines and their gradients.

 

[murraysp]

Hey man.

Look in the book there is a great diagram.

Basically the angle between the chords of P and both foci are equal.