The Curve Described Parametrically By x = T2 + t + 1, y = T2 – t + 1 Represents.

Slope of common tangent to parabolas y² = 4x and x² = 8y is

If a focal chord with positive slope of the parabola y² = 16xtouches the circle x² + y² – 12x + 34 = 0, then m is

If 2y = x + 24 is a tangent to parabola y² = 24x, then its distance from parallel normal is

PQ is a focal chord of the parabola y² = 4ax, O is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.

Find the shortest distance between the circle x² + y² – 24y + 128 = 0 and the parabola y² = 4x.

The equation of the directrix of the parabola y² + 4y + 4x + 2 = 0 is  

If the line x – 1 = 0 is the directrix of the parabola y² – ky + 8 = 0, then one of the of the value of k is

Equation of the parabola whose axis is y = x distance from origin to vertex is  and distance form origin to focus is , is (Focus and vertex lie in Ist quadrant) :

The focal chord of y² = 16x is tangent to (x – 6)² + y² = 2, then the possible values of the slope of this chord, are

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