Co Normal Points of ellipse

Find the equation of normal to the ellipse x^(2)+4y^(2)=4 at (2cos theta,sin theta). Hence,find the equation of normal to this ellipse which is parallel to the line 8x+3y=0.

Find the equation of normal to the ellipse x^(2)+4y^(2)=4 at (2 cos theta, sin theta) . Hence find the equation of normal to this ellipse which is paralel to the line 8x+3y=0 .

Find the locus of the mid-points of normal chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1

The maximum number of normals that can be drawn from any point to an ellipse, in general, is

Number of points on the ellipse x^2/a^2+y^2/b^2=1 at which the normal to the ellipse passes through at least one of the foci of the ellipse is

Prove that the tangent and normal at any point of an ellipse bisect the external and internal angles between the focal distances of the point