Search any question & find its solution
Question:
Answered & Verified by Expert
Find the length of the line-segment joining the vertex of the parabola $y^2=4 a x$ and a point on the parabola where the line-segment makes an angle $\theta$ to the $x$-axis.
Solution:
1762 Upvotes
Verified Answer
$$
\text { Let } \mathrm{P}(l \cos \theta, l \sin \theta) \text { lies on } y^2=4 a x
$$
$$
\begin{aligned}
&{\left[\because \cos \theta=\frac{\mathrm{OM}}{l} \Rightarrow \mathrm{OM}=l \cos \theta \sin \theta=\frac{\mathrm{PM}}{l}\right.} \\
&\left.\Rightarrow l^2 \sin ^2 \theta=4 a l \cos \theta \quad \Rightarrow \mathrm{PM}=l \sin \theta\right] \\
&\Rightarrow l=\frac{4 a \cos \theta}{\sin ^2 \theta}
\end{aligned}
$$
\text { Let } \mathrm{P}(l \cos \theta, l \sin \theta) \text { lies on } y^2=4 a x
$$
$$
\begin{aligned}
&{\left[\because \cos \theta=\frac{\mathrm{OM}}{l} \Rightarrow \mathrm{OM}=l \cos \theta \sin \theta=\frac{\mathrm{PM}}{l}\right.} \\
&\left.\Rightarrow l^2 \sin ^2 \theta=4 a l \cos \theta \quad \Rightarrow \mathrm{PM}=l \sin \theta\right] \\
&\Rightarrow l=\frac{4 a \cos \theta}{\sin ^2 \theta}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.