If the tangent at the point `(2sectheta, 3tantheta)` of the hyperbola `x^2/4-y^2/9=1`then the value of `theta`

If the tangent at the point (2sec theta,3tan theta) of the hyperbola (x^(2))/(4)-(y^(2))/(9)=1 then the value of theta

If the tangent at the point (2sec theta,3tan theta) to the hyperbola (x^(2))/(4)-(y^(2))/(9)=1 is parallel to 3x-y+4=0 , then the value of theta , is

sqrt(2)sectheta+tantheta=1

If the angle between the tangents at the end points of the chords of the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 is 90 then the locus of mid point of the chord of contact is

Tangent at point P (a sec theta, b tan theta) to the hyperbola meets the auxiliary circle of the hyper­bola at points whose ordinates are y_(1) and y_(2) , then 4b tan theta(y_(1)+y_(2))/(y_(1)y_(2)) is equal to

The triangular region bounded the tangent at the point P((pi)/(4)) on the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 and the pair of lines ((y)/(2)+(x)/(3))quad ((y)/(2)-(x)/(3))=0

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

tantheta-tantheta/2=sectheta/2

If tantheta + sectheta =p , then the value of sec theta is: