From the center `C` of hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` , perpendicular `C N` is drawn on any tangent to it at the point `P(asectheta,btantheta)` in the first quadrant. Find the value of `theta` so that the area of ` C P N` is maximum.

P is a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transvers axis at Tdot If O is the center of the hyperbola, then find the value of O TxO Ndot

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.

Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the x-axis. If tan alpha tan beta=1 , then find the value of c^(2)-d^(2) .

From the point (2,2) tangent are drawn to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1. Then the point of contact lies in the first quadrant (b) second quadrant third quadrant (d) fourth quadrant

If tangents drawn from the point (a,2) to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 are perpendicular, then the value of a^(2) is

If the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at at any point P(a sec theta,.b tan theta) meets the trans-verse axis in G,F is the foot of the perpendicular drawn from centre C to the normal at P then the geometric mean of PF and PG

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T . If O is the centre of the hyperbola, then OT . ON is equal to

If the angle between the asymptotes of hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 is 120^0 and the product of perpendiculars drawn from the foci upon its any tangent is 9, then the locus of the point of intersection of perpendicular tangents of the hyperbola can be (a)x^2+y^2=6 (b) x^2+y^2=9 (c)x^2+y^2=3 (d) x^2+y^2=18

Find the points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))= 2 from which two perpendicular tangents can be drawn to the circle x^(2) + y^(2) = a^(2)

P is a point on the hyperbola x^2/a^2-y^2/b^2=1 ; N is a foot of perpendicular from P on the transverse axis . The tangent to hyperbola at P meets the transeverse axis at T . If O is the center of the hyperbola ; then find the value of OTxxON.