For the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` , let `n` be the number of points on the plane through which perpendicular tangents are drawn. (a) If `n=1`,then `e=sqrt(2)` (b) If `n > 1`,then `1 < e < sqrt(2)` (c) If `n=0`, then `e > sqrt(2)` (d) None of these

For hyperbola x^2/a^2-y^2/b^2=1 , let n be the number of points on the plane through which perpendicular tangents are drawn.

The number of points outside the hyperbola x^2/9-y^2/16=1 from where two perpendicular tangents can be drawn to the hyperbola are: (a) 0 (b) 1 (c) 2 (d) none of these

For the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , distance between the foci is 10 units. Form the point (2, sqrt3) , perpendicular tangents are drawn to the hyperbola, then the value of |(b)/(a)| is

Number of point (s) outside the hyperbola x^(2)/25 - y^(2)/36 = 1 from where two perpendicular tangents can be drawn to the hyperbola is (are)

A parabola is drawn with focus at one of the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 . If the latus rectum of the ellipse and that of the parabola are same, then the eccentricity of the ellipse is (a) 1-1/(sqrt(2)) (b) 2sqrt(2)-2 (c) sqrt(2)-1 (d) none of these

The points on the ellipse (x^(2))/(2)+(y^(2))/(10)=1 from which perpendicular tangents can be drawn to the hyperbola (x^(2))/(5)-(y^(2))/(1) =1 is/are

If the tangents to the parabola y^2=4a x intersect the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at Aa n dB , then find the locus of the point of intersection of the tangents at Aa n dBdot

A normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 meets the axes at Ma n dN and lines M P and N P are drawn perpendicular to the axes meeting at Pdot Prove that the locus of P is the hyperbola a^2x^2-b^2y^2=(a^2+b^2)dot

The point of intersection of tangents drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 at the points where it is intersected by the line l x+m y+n=0 is

If the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 passes through the points (3sqrt2, 2) and (6, 2sqrt(3)) , then find the value of e i.e., eccentricity of the given hyperbola.