Equation of a common tangent to the circle, x2 + y2 – 6x = 0 and the parabola, y2 = 4x, is

Engineering

Mathematics

Tangent of Parabola

Question

Equation of a common tangent to the circle, x² + y² – 6x = 0 and the parabola, y² = 4x, is

$2y \sqrt{3} = 12x + 1$

$\sqrt{3} y = x + 3$

$2 \sqrt{3} y = - x - 12$

$\sqrt{3} y = 3x + 1$

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ty = x + t²

^{$| \frac{3 + t^{2}}{\sqrt{1 + t^{2}}} | = 3$}

^{$\Rightarrow t = \sqrt{3}$}

^{$\Rightarrow \sqrt{3} y = x + 3$}