If $(-2, 6)$ is the image of the point $(4, 2)$ with respect to the line $L = 0$,then $L$ is equal to

The equation of the line bisecting the line segment joining the points $(a, b)$ and $(a', b')$ at a right angle is

Find the equation of a line which passes through $(2 \cos^3 \theta, 2 \sin^3 \theta)$ and is perpendicular to the line $x \cos \theta - y \sin \theta = 2 \cos 2 \theta$.

Let a ray of light passing through the point $(3,10)$ reflect on the line $2x+y=6$ and the reflected ray pass through the point $(7,2)$. If the equation of the incident ray is $ax+by+1=0$,then $a^2+b^2+3ab$ is equal to:

$A$ person standing at the junction of two straight paths represented by the equations $2x - 3y + 4 = 0$ and $3x + 4y - 5 = 0$ wants to reach the path whose equation is $6x - 7y + 8 = 0$ in the least time. Find the equation of the path that he should follow.

If the image of the point $(3, 8)$ in the line $x + 3y = 7$ is $(\alpha, \beta)$,then $\alpha + \beta =$