The point of contact of the tangent to the parabolay2=9x which passes through the point (4, 10) andmakes an angle θ with the axis of the parabola suchthat tan⁡θ>2 is

Equation of the tangent at any point 9t2/4,9t/2on the parabola is ty=x+9t2/4. Since it passesthrough (4, 10), 10t=4+9t2/4 or 9t2−40t+16=0.⇒t=4/9,4⋅tan⁡θ=1/t>2⇒t<1/2. Sot=4/9 and the required point is (4/9, 2).