From the focus of the parabola $${y^2} = 12x$$, a ray of light is directed in a direction making an angle $${\tan ^{ - 1}}{3 \over 4}$$ with x-axis. Then the equation of the line along which the reflected ray leaves the parabola is

The point of contact of the tangent to the parabola y^{2} = 9x which passes through the point (4, 10) and makes an angle $$\theta$$ with the positive side of the axis of the parabola where tan$$\theta$$ > 2, is

A line passes through the point $$( - 1,1)$$ and makes an angle $${\sin ^{ - 1}}\left( {{3 \over 5}} \right)$$ in the positive direction of x-axis. If this line meets the curve $${x^2} = 4y - 9$$ at A and B, then |AB| is equal to

Let P be a point on (2, 0) and Q be a variable point on (y $$-$$ 6)^{2} = 2(x $$-$$ 4). Then the locus of mid-point of PQ is