Coordinate Geometry Questions

The circle passing through $(1,-2)$ and touching the axis of $x$ at $(3,0)$ also passes through the point:

Given: A circle, $2x^2+2y^2=5$ and a parabola, $y^2=4\sqrt{5}x$.Statement - I: An equation of a common tangent to these curves is $y=x+\sqrt{5}$.Statement - II: If the line $y=mx+\frac{\sqrt{5}}{m}$ ($m\ne 0$) is their common tangent, then $m$ satisfies $m^4-3m^2+2=0$.

A ray of light along $x+\sqrt{3}y=\sqrt{3}$ gets reflected upon reaching $x$ -axis, the equation of the reflected rays is:

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, and having centre at $(0,3)$ is:

The $x$ -coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0,1)$, $(1,1)$ and $(1,0)$ is:

If the lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{k}$ and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, then $k$ can have:

Distance between two parallel planes $2x+y+2z=8$ and $4x+2y+4z+5=0$ is: