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)))

If tangents are drawn to the ellipse 2x^(2) + 3y^(2) =6 , then the locus of the mid-point of the intercept made by the tangents between the co-ordinate axes is

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

If a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 makes equal intercepts of length l on cordinates axes, then the values of l is

Tangents are drawn from the point P(-sqrt(3),sqrt(2)) to an ellipse 4x^(2)+y^(2)=4 Statement-1: The tangents are mutually perpendicular.and Statement-2: The locus of the points can be drawn togiven ellipse is x^(2)+y^(2)=5

Find the equation of the tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 which makes equal intercepts on the axes

Any tangent to an ellips (x^(2))/(a^(2))+(y^(2))/(b^(2))=1, (a gt b) cut by the tangents at the end points of major axis is T and T' . Prove that the length of intercept of the major axis cut by the circle describe on T T' as diameter is constant and equal to 2sqrt(a^(2)-b^(2)) .