Parabola - Coordinate Geometry - Mathematics Previous Year Questions

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

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

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

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