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)`

Three normals drawn from a point (h k) to parabola y^2 = 4ax

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)

The locus of the mid-points of the chords of the ellipse x^2/a^2+y^2/b^2 =1 which pass through the positive end of major axis, is.

If the normal from the point P(h,1) on the ellipse x^2/6+y^2/3=1 is perpendicular to the line x+y=8 , then the value of h is

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 length ofthe normal (terminated by the major axis) at a point of the ellipse x^2/a^2+y^2/b^2=1 is

If the normal at an end of latus rectum of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 passes through the point (0, 2b) then

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 equation of the ellipse whose centre is at origin and which passes through the points (-3,1) and (2,-2) is

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