Question

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

• A. $\frac{8}{3}$
• B. $8$
• C. $\frac{16}{3}$
• D. $4$

Answer 1

The correct option is B $8$

$y^2=12x$

Equation of chord passing through vertex $(0,0)$ and making an angle ${60}^{\circ }$ with $x-axis$ is $y=\sqrt{3}x$

$y^2=12x⟹3x^2=12x⟹x=0,4$

The point of intersection of chord with parabola is $(4,4\sqrt{3})$

Length of common chord is $\sqrt{16+48}=8$