The point of intersection of two tangents to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` , the product of whose slopes is `c^2,` lies on the curve: `y^2-b^2=c^2(x^2+a^2)` (B) `y^2+a^2=c^2(x^2-b^2)` (C) `y^2+b^2=c^2(x^2-a^2)` (D) `y^2-a^2=c^2(x^2+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

If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then a^2-b^2 is equal to (A) 1/(a^2e^2) (B) a^2e^2 (C) b^2e^2 (D) none of these

If a x+b y=1 is tangent to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then a^2-b^2 is equal to (a) 1/(a^2e^2) (b) a^2e^2 (c) b^2e^2 (d) none of these

The condition that the line y=mx+c may be a tangent to (y^(2))/(a^(2))-x^(2)/b^(2)=1 is

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

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

If e and e' are the eccentricities of the hyperbola x^2/a^2-y^2/b^2=1 and y^2/b^2-x^2/a^2=1, then the point (1/e,1/(e')) lies on the circle (A) x^2+y^2=1 (B) x^2+y^2=2 (C) x^2+y^2=3 (D) x^2+y^2=4

Which of the following can be slope of tangent to the hyperbola 4x^2-y^2=4? (a) 1 (b) -3 (c) 2 (d) -3/2

The locus of the poles of the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 w.r.t. the circle x^2 + y^2 = a^2 is: (a) parabola (b) ellipse (c) hyperbola (d) circle

Locus of all such points from where the tangents drawn to the ellipse x^2/a^2 + y^2/b^2 = 1 are always inclined at 45^0 is: (A) (x^2 + y^2 - a^2 - b^2)^2 = (b^2 x^2 + a^2 y^2 - 1) (B) (x^2 + y^2 - a^2 - b^2)^2 = 4(b^2 x^2 + a^2 y^2 - 1) (C) (x^2 + y^2 - a^2 - b^2)^2 = 4(a^2 x^2 + b^2 y^2 - 1) (D) none of these