The minimum length of intercept of any tangent of ellipse `x^2/a^2 + y^2/b^2 = 1` between axes is : (A) `2a` (B) `2b` (C) `a+b` (D) `a-b`

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)

The locus of mid points of parts in between axes and tangents of ellipse x^2/a^2 + y^2/b^2 =1 will be

The minimum length of intercept on any tangent to the ellipse (x^(2))/(4)+(y^(2))/(9)=1 cut by the circle x^(2)+y^(2)=25 is :

The locus of mid point of tangent intercepted between area of ellipse x^2/a^2 +y^2/b^2 = 1 is

The locus of the middle point of the portion of a tangent to the ellipse x^2/a^2+y^2/b^2=1 included between axes is the curve

The product of the perpendicular from two foci on any tangent to the hyperbola x^2/a^2-y^2/b^2=1 is (A) a^2 (B) (b/a)^2 (C) (a/b)^2 (D) b^2

Length of common tangents to the hyperbolas x^2/a^2-y^2/b^2=1 and y^2/a^2-x^2/b^2=1 is

The locus of the middle points of the portions of the tangents of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 included between the axis is the curve (a)    (x^2)/(a^2)+(y^2)/(b^2)=1/4 (b)    (a^2)/(x^2)+(b^2)/(y^2)=4 (c)    a^2x^2+b^2y^2=4 (d)    b^2x^2+a^2y^2=4

Show that the length of the chord intercepted by the ellipse x^2/a^2 + y^2/b^2 = 1 on the line y= mx + c is 2ab/(a^2 m^2 + b^2) sqrt((1+m^2) (a^2 m^2 + b^2 - c^2))

show that the locus of the middle points of portions of the tangents to the hyperbola x^2/a^2 - y^2/b^2 = 1 intercepted between the axes is 4x^2 y^2 = a^2 y^2 - b^2 x^2 .