From the centre C of the hyperbola `(x^(2))/(16)-(y^(2))/(9)=1`, perpendicular CN is drawn on any tangent to it at the point P in the first quadrant. Find the maximum area of triangle CPN.

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.

The centre of the hyperbola 9x^2-16y^2-18x+64y-199=0 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 _____

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

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 x^2+y^2=3 (d) x^2+y^2=18

With one focus of the hyperbola x^2/9-y^2/16=1 as the centre, a circle is drawn which is tangent to the hyperbola with no part of the circle being outside the hyperbola. The radius of the circle is

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , and 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

Find the equation of pair of tangents drawn from point (4, 3) to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 . Also, find the angle between the tangents.

On which curve does the perpendicular tangents drawn to the hyperbola (x^(2))/(25)-(y^(2))/(16)=1 intersect?

Tangents are drawn to the hyperbola 4x^2-y^2=36 at the points P and Q. If these tangents intersect at the point T(0,3) then the area (in sq units) of triangle PTQ is