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 _____

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.

The number of tangents drawn from point (-5,3) to the hyperbola (x^2)/(25)-(y^2)/9=1 are 0 (2) 1 (3) 2 3 (5) 4

Tangents drawn from a point on the circle x^2+y^2=9 to the hyperbola x^2/25-y^2/16=1, then tangents are at angle

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 .

Statement- 1 : Tangents drawn from the point (2,-1) to the hyperbola x^(2)-4y^(2)=4 are at right angle. Statement- 2 : The locus of the point of intersection of perpendicular tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is the circle x^(2)+y^(2)=a^(2)-b^(2) .

Statement-I Two tangents are drawn from a point on the circle x^(2)+y^(2)=9 to the hyperbola (x^(2))/(25)-(y^(2))/(16)=1 , then the angle between tangnets is (pi)/(2) . Statement-II x^(2)+y^(2)=9 is the directrix circle of (x^(2))/(25)-(y^(2))/(16)=1 .

Find the equaiton of the tangents to the hyperbola x^2 - 2y^2 = 18 which are perpendicular to the line x-y=0 .

Tangents are drawn from the point (4, 2) to the curve x^(2)+9y^(2)=9 , the tangent of angle between the tangents :

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