few Qs from 4unit s.k patel im having problems with.. (1 Viewer)

[suneeta =)]

Show that the equation of the normal to the ellipse x^2/a^2 + y^2/b^2 = 1 at P( acosX , bsinX ) is given by axsinX - bycosX = (a^2 - b^2)sinXcosX.
The normal at P meets the x-axis at M and N is the foot of the perpendicular PN to the axis. Prove that MN = (b^2.cosX)/a

Show that the tangent to the ellipse x^2/a^2 + y^2/b^2 = 1 at P(x1, y1) has the equation (x.x1)/a^2 + (y.y1)/b^2 = 1 . This tangent meets the x-axis at T. PN is perpendicular to the x-axis at G. Show that OT x NG = b^2, where O is the centre of the ellipse.



I get how to do the "show the equation of etc etc" but I'm having problems with the latter parts of the questions.

Any help would be appreciated

 

[js992]

Find your coordinates of M and N

Your distance MN is ON -OM

 

[js992]

Show that the tangent to the ellipse x^2/a^2 + y^2/b^2 = 1 at P(x1, y1) has the equation (x.x1)/a^2 + (y.y1)/b^2 = 1 . This tangent meets the x-axis at T. PN is perpendicular to the x-axis at G. Show that OT x NG = b^2, where O is the centre of the ellipse.

Find Coordinates T, N and G

 

[suneeta =)]

Thankyouuuu !