If the line `y=mx + sqrt(a^2 m^2 - b^2)` touches the hyperbola `x^2/a^2 - y^2/b^2 = 1` at the point `(a sec phi, b tan phi)`, show that `phi = sin^(-1) (b/am)`.

If the line y = mx + sqrt(a^(2)m^(2) - b^(2)) touches the hyperbola x^(2)/a^(2) - y^(2)/b^(2) = 1 at the point (a sec theta, b tan theta) , then find theta .

If the line y = mx + sqrt(a^(2) m^(2) -b^(2)), m = (1)/(2) touches the hyperbola (x^(2))/(16)-(y^(2))/(3) =1 at the point (4 sec theta, sqrt(3) tan theta) then theta is

(sec phi-tan phi)^2 (1+sin phi)^2 div sin^2 phi =?

If the chord through the points (a sec theta, b tan theta) and (a sec phi, b tan phi) on the hyperbola x^2/a^@ - y^2/b^2 = 1 passes through a focus, prove that tan theta/2 tan phi/2 + (e-1)/(e+1) = 0 .

Show that the equation of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (a sqrt(2),b) is ax+b sqrt(2)y=(a^(2)+b^(2))sqrt(2)

Let P(a sec theta,b tan theta) and Q(a sec c phi,b tan phi) (where theta+phi=(pi)/(2) be two points on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 If (h,k) is the point of intersection of the normals at P and Q then k is equal to (A) (a^(2)+b^(2))/(a)(B)-((a^(2)+b^(2))/(a))( C) (a^(2)+b^(2))/(b)(D)-((a^(2)+b^(2))/(b))