The angle of intersection of the parabolas y2 = 4 ax and x2 = 4ay at the origin is ____________ .

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KollegeApply · Accepted Answer

$\pi$/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 dy/dx = 4a \Rightarrow dy/dx = 2a/y \Rightarrow m_1 = \infty \text { Now, on differentiating (2) w.r.t.x, we get } 2x = 4ady/dx \Rightarrow dy/dx = x/2a = 0 \therefore \tan $\theta$ = \left| m_1 - m_2/1 + m_1 m_2 \right| = \left| \infty/1 + 0 \right| = \infty \Rightarrow $\theta$ = \tan^{- 1} \infty = $\pi$/2

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