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 T×O Ndot

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 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 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

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

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 (a) first quadrant (b) second quadrant (c) third quadrant (d) fourth quadrant

C is the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 The tangent at any point P on this hyperbola meet the straight lines b x-a y=0 and b x+a y=0 at points Qa n dR , respectively. Then prove that C QdotC R=a^2+b^2dot

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.