If the tangents drawn through the point `(1, 2 sqrt(3)` to the ellipse `x^2/9 + y^2/b^2 = 1` are at right angles, then the value of `b` is (A) `1` (B) `-1` (C) `2` (D) `4`

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 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

If two tangents drawn from a point P to the parabola y^2=4x are at right angles, then the locus of P is (a) 2x+1=0 (b) x=-1 (c) 2x-1=0 (d) x=1

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)

Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/4=1 touching the ellipse at point A and B. Q. The coordinates of A and B are

The line y=mx+1 is a tangent to the curve y^2=4x if the value of m is(A) 1 (B) 2(C) 3(D) 1/2.

The length of perpendicular from the centre to any tangent of the ellipse x^2/a^2 + y^2/b^2 =1 which makes equal angles with the axes, is : (A) a^2 (B) b^2 (C) sqrt(a^2-b^2)/2) (D) sqrt((a^2 + b^2)/2)

If the chords of contact of tangents fromtwo points (x_1,y_1) and (x_2,y_2) to the hyperbola x^2/a^2-y^2/b^2=1 are at right angles, then (x_1x_2)/(y_1y_2) is equal to (a) a^2/(-b^2) (b) b^2/(-a^2) (c) b^4/(-a^4)

The tangent at any point P on the ellipse meets the tangents at the vertices A & A^1 of the ellipse x^2/a^2 + y^2/b^2 = 1 at L and M respectively. Then AL.A^1M = (A) a^2 (B) b^2 (C) a^2+b^2 (D) ab

Statement-1: Tangents drawn from any point on the circle x^(2)+y^(2)=25 to the ellipse (x^(2))/(16)+(y^(2))/(9)=1 are at right angle Statement-2: The locus of the point of intersection of perpendicular tangents to an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is its director circle x^(2)+y^(2)=a^(2)+b^(2) .