A chord is drawn through the focus of the parabola y2 = 6x such than its distance from the vertex of this parabola is 52 , then its slope can be

Focus of the parabola is $(\frac{3}{2}, 0)$ Let the equation of the chord be

$y = m (x - \frac{3}{2})$

Its distance from the vertex $(0, 0)$ is $|\frac{- \frac{3 m}{2}}{\sqrt{1 + m^{2}}}| = \frac{\sqrt{5}}{2}$

$\Rightarrow 9 m^{2} = 5 (1 + m^{2})$

$\Rightarrow m^{2} = \frac{5}{4} \Rightarrow m = \frac{\sqrt{5}}{2}$

A chord is drawn through the focus of the parabola $y^{2} = 6 x$ such than its distance from the vertex of this parabola is
$\frac{\sqrt{5}}{2}$ , then its slope can be