If the double ordinate of the parabola $y^2=8 x$ is of length 16 , then the angle subtended by it at the vertex of the parabola is

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Aicharya · Accepted Answer

Let $A\left(x_1, y_1ight)$ and $B\left(x_1,-y_1ight)$ are the co-ordinate of end points of double ordinate length of $A B=2 y_1=16$ $ A\left(x_1, 8ight) 	ext { and } B\left(x_1,-8ight) $ $A$ and $B$ lies on parabola. So, $ 64=8 x_1 \Rightarrow x_1=8 $ So, coordinate of $A$ and $B$ are $(8,8),(8,-8)$ $ \begin{aligned} \Rightarrow \quad 	an \alpha & =\frac{8}{8}=1 \ \alpha & \left.=\frac{\pi}{4} \quad 	ext { (Angle with } X 	ext {-axis made by } O Aight) \end{aligned} $ Angle subtended by double ordinate $A B$ at vertex $ \begin{aligned} & =2 \alpha \ & =2 \cdot \pi / 4=\pi / 2 \end{aligned} $

If the double ordinate of the parabola $y^2=8 x$ is of length 16 , then the angle subtended by it at the…

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