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 _____

Find the angle between the asymptotes of the hyperbola (x^2)/(16)-(y^2)/9=1 .

How many real tangents can be drawn from the point (4, 3) to the hyperbola (x^2)/(16)-(y^2)/9=1? Find the equation of these tangents and the angle between them.

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.

If the distance between two parallel tangents having slope m drawn to the hyperbola (x^2)/9-(y^2)/(49)=1 is 2, then the value of 2|m| is_____

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) .

Find the equation of the two tangents from the point (1,2) to the hyperbola 2x^(2)-3y^2=6

If two distinct tangents can be drawn from the point (alpha, alpha+1) on different branches of the hyperbola (x^(2))/(9)-(y^(2))/(16)=1 , then find the values of alpha .

If the chords of contact of tangents from two points (-4,2) and (2,1) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 are at right angle, then find then find the eccentricity of the hyperbola.

Find the equations of the tangents drawn from the point (2, 3) to the ellipse 9x^2+16 y^2=144.

The area of triangle formed by the tangents from the point (3, 2) to the hyperbola x^2-9y^2=9 and the chord of contact w.r.t. the point (3, 2) is_____________