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

A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c. the locus of P is a

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 L₁ and L₂ are the length of the segments of any focal chord of the parabola y² = x, then  is equal to

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