If a tangent of the circle $x^2+y^2+2 x+2 y+1=0$ is radical axis of the circles $x^2+y^2+2 g x+2 f y+c=0$ and $2 x^2+2 y^2+3 x+8 y+2 c=0$, then

If the angle between the tangents drawn to the parabola $y^2=4 x$ from the points on the line $4 x-y=0$ is $\frac{\pi}{3}$, then the sum of the abscissae of all such points is

The normal at a point on the parabola $y^2=4 x$ passes through a point $P$. Two more normals to this parabola also pass through $P$. If the centroid of the triangle formed by the feet of these three normals is $G(2,0)$, then the abscissa of $P$ is

The circumcenter of the equilateral triangle having the three points $\theta_1, \theta_2, \theta_3$ lying on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ as its vertices is $(r, s)$. Then, the average of $\cos \left(\theta_1-\theta_2\right)$, $\cos \left(\theta_2-\theta_3\right)$ and $\cos \left(\theta_3-\theta_1\right)$ is