If L1 and L2 are The Length Of The Segments Of Any Focal Chord Of The Parabola y2 = x, Then  is Equal To

Shortest distance of the point (0, c) from the parabola y = x²where  is

The length of the intercept on the normal at the point (at², 2at) of the parabola y² = 4ax made by the circle which is described on the focal distance of the given point as diameter is 

A line bisecting the ordinate PN of a point P(at², 2at), t > 0, on the parabola y² = 4ax is drawn parallel to the axis to meet the curve at Q. If NQ meets the tangent at the vertex at the point T, then the coordinates of T are.

If P, Q, R are three points on a parabola y² = 4ax whose ordinates are in geometrical progression, then the tangents at P and R meet on

The tangents at three points A, B, C on the parabola y² = 4x, taken in pairs intersect at the points P, Q and R. If  be the areas of the triangles ABC and PQR respectively, then 

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y² = 4ax is another parabola with directrix

Equation of a common tangent to the curves y² = 8x and xy = –1 is 

The tangent at the point P(x₁, y₁) to the parabola y² = 4ax meets the parabola y² = 4a(x + b) at Q and R, the coordinates of the mid-point of QR are