Q. Show that the feet of normals from a point (h, K) to the ellipse `x^2/a^2+y^2/b^2=1` lie on a conic which passes through the origin & the point `(h, k)`

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 chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

Prove that the chord of contact of tangents drawn from the point (h,k) to the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 will subtend a right angle at the centre, if h^(2)/a^(4)+k^(2)/b^(4)=1/a^(2)+1/b^(2)

Prove that the feet of the normals drawn from the point (h, k) to the parabola y^2 -4ax lie on the curve xy-(h-2a)y-2ak=0 .

The chords of contact of the pair of tangents drawn from each point on the line 2x + y=4 to the circle x^2 + y^2=1 pass through the point (h,k) then 4(h+k) is

The chords of contact of the pair of tangents drawn from each point on the line 2x + y=4 to the circle x^2 + y^2=1 pass through the point (h,k) then 4(h+k) is

The feet of the normals to (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 from (h,k) lie on

The feet of the normals to (x^(2))/(a^(2)) -(y^(2))/(b^(2)) =1 from (h,k) lie on

The equation of the curve, slope of whose tangent at any point (h, k) is 2k/h and which passes through the point (1, 1) is