You're good for . Isn't that the point?
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!
In the problem, it is stated that the ordinate at P and the tangent at P meet the asymptote at Q and R respectively.
I presume that the point Q lies on the asymptote y = bx/a, and R lies on the asymptote y = -bx/a.
The x co-ordinate of Q is the same as the x co-ordinate of P. Only ordinate will change. So the slope of RQ is not equal to b/a.