Angle subtended by double ordinate of parabola

Question

Angle subtended by double ordinate of length 32√3 of the parabola 

x²-6x+16y+25=0 at the vertex is 

Answer 1

Let PQ be the Ordinate.

Hence P has y- coordinate

= 4a, as y²= 4ax

\(\Rightarrow x = \frac{y^2}{4a}= \frac{(4a)^2}{4a}=4a\)

\(\Rightarrow\) In \(\Delta OMP,\)

\(tan\theta=\frac{4a}{4a}=1\)

\(\Rightarrow\theta=45^\circ\)

\(\Rightarrow\angle POQ=2\theta=90^\circ\)