Equation of the line passing through points of intersection of the parabola $y^{2} = 8 x$ and ellipse $x^{2} + \frac{y^{2}}{3} = 1$ is

x - 3 = 0

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x + 3 = 0

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3y + 1 =0

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3x - 1 =0

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Solution

The correct option is D 3x - 1 =0
Parabola is $y^{2} = 8 x$ ....(1) $(x \geq 0)$
Ellipse is $x^{2} + \frac{y^{2}}{3} = 1$ ...(2)
Solving (1) & (2), $x^{2} + \frac{8 x}{3} = 1$
$\Rightarrow 3 x 2 + 8 x - 3 = 0$
$\Rightarrow (3 x - 1) (x + 3) = 0$
$\Rightarrow 3 x - 1 = 0, x + 3 \neq 0$
$∴$ Equation of required line is 3x - 1 = 0

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