Struggling With Conics Question (1 Viewer)

[Jacobagel]

Consider the general equation for an ellipse. Point P(acostheta, bsintheta) is a point on the ellipse, where costheta and sintheta do not equal to 0. The normal at P meets the major axis at G and the minor axis at H. R is the point (0, bsintheta) on the minor axis, and O is the centre of the ellipse.

Prove that PG : PH = RO : RH

 

[Trebla]

Draw a diagram and it should be clear that you just need to prove similar triangles and equate the ratio of sides, then work it out from there.

Alternatively, you could find the coordinates of G and H then directly prove the ratio by computation.

 

[Jacobagel]

Ok, thanks. I guess I was just lazy to draw a diagram. Would you recommend drawing a diagram if it isn't given for the question?

 

[HeroWise]

Yes