The common tangent to circle $x^{2} + y^{2} = 2$ and parabola $y^{2} = 8 x$ and lying below x-axis is equal to

y = x + 1

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y = x + 2

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y = x - 2

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y = - x - 2

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Solution

The correct option is D $y = - x - 2$
Tangent to parabola is $y = m x + \frac{2}{m}$
If it is also tangent to circle
$∴ ∣ ∣ ∣ \frac{2 / m}{\sqrt{1 + m^{2}}} ∣ ∣ ∣ = \sqrt{2} \Rightarrow m = \pm 1$
$∴$ Equation of tangent is
$∴ y = x + 2$
or $y = - x - 2$
$∴$ Tangent below x - axis is $y = - x - 2$ .

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The common tangent to circle x2+y2=2 and parabola y2=8x and lying below x-axis is equal to

The correct option is D y=−x− 2Tangent to parabola is y=mx+2mIf it is also tangent to circle ∴∣∣∣2/m√1+m2∣∣∣=√2⇒m=±1∴ Equation of tangent is ∴y=x+2or y=−x−2∴ Tangent below x - axis is y=−x−2.

The common tangent to circle $x^{2} + y^{2} = 2$ and parabola $y^{2} = 8 x$ and lying below x-axis is equal to