Parabola

For the parabola $y^2=16 x$, length of a focal chord, whose on end point is $(16,16)$ is $L^2$, then absolute value of $L$ is

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

The point $(-2 m, m+1)$ is an interior point of the smaller region bounded by circle $x^2+y^2=4$ and the parabola $y^2=4 x$, then

The area of circle touching parabola $y=x^2$ at $(1,1)$ and having directrix of $y=x^2$ as its normal is $125 A \pi$, then $A$ is

If the 4th term in the expansion of \(\left(p x+\frac{1}{x}\right)^n, n \in N\) is \(\frac{5}{2}\) and three normals to the parabola \(y^2=x\) are drawn through a point \((q, 0)\), then

If the tangent at \(P\) on \(y^2=4 a x\) meets the tangent at the vertex in \(Q\) and \(S\) is the focus of the parabola, then \(\angle S Q P\) is equal to

The locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to its distance from a fixed straight line in the same plane represents