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+2y^2=2 , then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

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)))

Show that the point (2,(2)/(sqrt(5))) lies on the ellipse 4x^(2) + 5y^(2) = 20 . Show further that the sum of its distances from the two foci is equal to the length of its major axis .

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.

The angle between the pair of tangents drawn to the ellipse 3x^(2) + 2y^(2) =5 from the point (1, 2) is-

Find the equation of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at ( a sec, theta b tan theta) . Hence show that if the tangent intercepts unit length on each of the coordinate axis than the point (a,b) satisfies the equation x^(2)-y^(2)=1

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

If two points are taken on the minor axis of an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 at the same distance from the center as the foci, then prove that the sum of the squares of the perpendicular distances from these points on any tangent to the ellipse is 2a^2dot

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