The equation of the parabola whose focus is $(6,0)$ and directrix is $x=-6$ is

Find the angle of intersection of the curves $y^2 = 4x$ and $x^2 = 4y$.

The shortest distance between the line $y-x=1$ and the curve $x=y^2$ is

If the vertices of a triangle are $(am_1^2, 2am_1), (am_2^2, 2am_2),$ and $(am_3^2, 2am_3),$ then the area of the triangle is

Let $C$ be the locus of the mirror image of a point on the parabola $y^{2}=4x$ with respect to the line $y=x$. Then the equation of the tangent to $C$ at $P(2,1)$ is:

Let $P, Q,$ and $R$ be three co-normal points on the parabola $y^2 = 4ax$. Then the correct statement$(s)$ is/are: