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प्रश्न
The angle of intersection of the parabolas y2 = 4 ax and x2 = 4ay at the origin is ____________ .
विकल्प
π/6
π/3
π/2
π/4
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उत्तर
π/2
\[\text { Given }: \]
\[ y^2 = 4ax . . . \left( 1 \right)\]
\[ x^2 = 4ay . . . \left( 2 \right)\]
\[\text { Point } =\left( 0, 0 \right)\]
\[\text { On differentiating (1) w.r.t.x,we get }\]
\[2y \frac{dy}{dx} = 4a\]
\[ \Rightarrow \frac{dy}{dx} = \frac{2a}{y}\]
\[ \Rightarrow m_1 = \infty \]
\[\text { Now, on differentiating (2) w.r.t.x, we get }\]
\[2x = 4a\frac{dy}{dx}\]
\[ \Rightarrow \frac{dy}{dx} = \frac{x}{2a} = 0\]
\[ \therefore \tan \theta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} \right| = \left| \frac{\infty}{1 + 0} \right| = \infty \]
\[ \Rightarrow \theta = \tan^{- 1} \infty = \frac{\pi}{2}\]
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