Find the area of the triangle formed by any tangent to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` with its asymptotes.

Find the value of m for which y=m x+6 is tangent to the hyperbola (x^2)/(100)-(y^2)/(49)=1

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0), y_(0)).

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

Find the product of the length of perpendiculars drawn from any point on the hyperbola x^2-2y^2-2=0 to its asymptotes.

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

Find the value of c if y = x + c is a tangent to the hyperbola 9x^(2) -16y^(2) = 144

If the latus rectum subtends a right angle at the center of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , then find its eccentricity.

Find the equations to the common tangents to the two hyperbolas (x^2)/(a^2)-(y^2)/(b^2)=1 and (y^2)/(a^2)-(x^2)/(b^2)=1

Find the area of the triangle formed by the lines joining the vertex of the parabola x^2 = 12y to the ends of its latus rectum.