is a point on the hyperbola . The ordinate at P and the tangent at P meet the asymptote at Q and R respectively. if the normal at P meets the x-axis at N prove that RQ and QN are perpendicular.

The ordinate at P is its y-value.

Asymptotes:

when ,

equation of tangent

when

equation of normal

when y=0,

gradient RQ

gradient QN

my problem is i can't get the product of the two gradients to be -1.

thanks!