The point of intersection of the normals to the parabola $y^2 = 4x$ at the ends of its latus rectum is

What is the length of the chord of contact of the tangents drawn from the point $(-2, -1)$ to the parabola $y^2 = 4x$?

Find the area of the triangle formed by the points $(at_1^2, 2at_1)$,$(at_2^2, 2at_2)$,and $(at_3^2, 2at_3)$.

Statement $I$: $4x^2+y^2-4xy-30x-50y+40=0$ is the equation of a parabola having $(2,3)$ as its focus and $x+2y+5=0$ as its directrix.
Statement $II$: The equation of the directrix of the parabola $x^2-4x+16y+52=0$ is $y+1=0$.
Which of the above statements is (are) true?

The focal chord to $y^2 = 16x$ is tangent to $(x - 6)^2 + y^2 = 2$. Then,the possible values of the slope of this chord are:

The points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line