Inclination of a Line

Q. Let $P=(-1,0),Q=(0,0),andR=(3,3\sqrt{3})$ be three points. Then the equation of the bisector of $\angle PQR$ is

1. $\left(\frac{\sqrt{3}}{2}\right)x+y=0$
2. $x=\sqrt{3}y=0$
3. $\sqrt{3}x+y=0$
4. $x+\left(\frac{\sqrt{3}}{2}\right)y=0$

Q. The gradient of the line joining the points on the curve $y=x^2+2x$ whose abscissa are 1 and 3, is

1. 6
2. 5
3. 4
4. 3

Q. Find the length of the segment joining the vertex of the parabola $y^2=ax$ and a point on the parabola where the line segment makes an angle ${}^{\prime }{\theta }^{\prime }$ to the x-axis.

1. $\frac{2a\cos \theta }{{\sin }^2\theta }$
2. None of the above
3. $\frac{4a\cos \theta }{{\sin }^2\theta }$
4. $\frac{4a\cos \theta }{3{\sin }^2\theta }$