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.

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

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

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 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.

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.

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

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 _____