The line $2 a x + b y + 3 c = 0$ passes through points of intersection of parabola $y^{2} = 4 x, x^{2} = 4 y$ then_______

4 c^{2} + (a + b)^{2} = 0

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9 c^{2} + (2 b + a)^{2} = 0

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c^{2} + (2 a - b)^{2} = 0

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c^{2} + (2 a + b)^{2} = 0

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Solution

The correct option is D $c^{2} + (2 a + b)^{2} = 0$
$\begin{matrix} f r o m t h e g r a p h l i n e p a s sin g t h r o u g h i n t e r s e c t i o n o f p a r a b o l a y = x \Rightarrow y - x = 0 - - - (1) 2 a x + b y + 3 c = 0 - - - (2) c o m p a r i n g a = \frac{- 1}{2}, b = 1, c = 0 ∴ c^{2} + {(2 a + b)}^{2} = 0 H e n c e, t h e o p t i o n D i s t h e c o r r e c t a n s w e r . \end{matrix}$

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