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  4. The length of the chord of the parabola, y2=12 x passing through the vertex making an angle of 60° with the axis of x is:

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Q. The length of the chord of the parabola, $y^2=12 x$ passing through the vertex \& making an angle of $60^{\circ}$ with the axis of $x$ is:

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Solution:

Length of chord $=\frac{4}{m^2} \sqrt{a(a-m c)\left(1+m^2\right)}$
$m=\tan 60^{\circ}=\sqrt{3}$
Length of chord $=\frac{4}{3} \sqrt{3(3-\sqrt{3} \times 0)(1+3)}=\frac{4}{3} \sqrt{36}=8$