Tangents are drawn to the ellipse from the point `((a^2)/(sqrt(a^2-b^2)),sqrt(a^2+b^2)))` . Prove that the tangents intercept on the ordinate through the nearer focus a distance equal to the major axis.

Tangent are drawn from the point (-1,2) on the parabola y^2=4x . Find the length that these tangents will intercept on the line x=2.

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

Find the points on the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 such that the tangent at each point makes equal angles with the axes.

if tangents are drawn to the ellipse x^(2)+2y^(2)=2 all points on the ellipse other its four vertices then the mid-points of the tangents intercepted between the coorinate axs lie on the curve

A tangent is drawn at any point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 . If this tangent is intersected by the tangents at the vertices at points P and Q, then which of the following is/are true

The tangents and normal at a point on (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 cut the y-axis A and B. Then the circle on AB as diameter passes through

A hyperbola passes through the point (sqrt2,sqrt3) and has foci at (+-2,0) . Then the tangent to this hyperbola at P also passes through the point:

Tangents are drawn from any point on the circle x^(2)+y^(2) = 41 to the ellipse (x^(2))/(25)+(y^(2))/(16) =1 then the angle between the two tangents is

Statement 1 : Tangents are drawn to the ellipse (x^2)/4+(y^2)/2=1 at the points where it is intersected by the line 2x+3y=1 . The point of intersection of these tangents is (8, 6). Statement 2 : The equation of the chord of contact to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 from an external point is given by (x x_1)/(a^2)+(y y_1)/(b^2)-1=0