The tangents from `(x_1 , y_1)` to the ellipse `x^2/a^2+y^2/b^2=1`.intersect at right angles. Show that the normals at the points of contact meet on the line `y/y_1=x/x_1`

The tangents from (alpha, beta) to the ellipse x^2/a^2 + y^2/b^2 = 1 intersect at right angle. Show that the locus of the point of intersection of normals at the point of contact of the two tangents is the line ay-betax=0 .

If the tangents from the point (lambda, 3) to the ellipse x^2/9+y^2/4=1 are at right angles then lambda is

If the tangents from the point (lambda, 3) to the ellipse x^2/9+y^2/4=1 are at right angles then lambda is

If the tangents from the point (lambda, 3) to the ellipse x^2/9+y^2/4=1 are at right angles then lambda is

If the tangents drawn from a point (1,2 sqrt(3)) to the ellipse (x^(2))/(9)+(y^(2))/(b^(2))=1 are at right angles then b =

If the tangents from the point (lambda,3) to the ellipse (x^(2))/(9)+(y^(2))/(4)=1 are at right angles then lambda is

The line x = at^(2) meets the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 in the real points iff

If the chords of contact of tangents from two poinst (x_1, y_1) and (x_2, y_2) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 are at right angles, then find the value of (x_1x_2)/(y_1y_2)dot