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

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 position of the point (6,-5) with respect to the hyperbola (x^(2))/(9)-(y^(2))/(25) = 1

Show that the locus of the midpoints of the chords of the circle x^(2)+y^(2)=a^(2) which are tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is (x^(2)+y^(2))^(2)=a^(2)x^(2)-b^(2)y^(2) .

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x0, y0).

Find the equation of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at ( a sec, theta b tan theta) . Hence show that if the tangent intercepts unit length on each of the coordinate axis than the point (a,b) satisfies the equation x^(2)-y^(2)=1

Find the value of m, for which the line y=mx + 25sqrt3/3 is a normal to the conic x^2 /16 - y^2 / 9 =1 .

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

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 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 that can be drawn from the point (6, 2) on the hyperbola (x^(2))/(9)-(y^(2))/(4)=1 is