The point of contact of the tangent to the parabola

$y^2=9x$ which passes through the point (4, 10) and
makes an angle $\theta$ with the axis of the parabola such
that $\tan \theta >2$ is 

Equation of the tangent at any point $\left(9t^2/4,9t/2\right)$

on the parabola is $ty=x+9t^2/4$. Since it passes
through (4, 10), $10t=4+9t^2/4\text{ or }9t^2-40t+16$

=0.

$\Rightarrow t=4/9,4\cdot \tan \theta =1/t>2\Rightarrow t<1/2$. So

$t=4/9$ and the required point is (4/9, 2).