Consider The Two Curves C1 : y2 = 4x, C2 : x2 + y2 – 6x + 1 = 0. Then,

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 curve described parametrically by x = t² + t + 1, y = t² – t + 1 represents.

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

If  and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y² = 4ax and x² = 4ay, then

Let P be the point (1, 0) and Q a point on the locus y² = 8x. The locus of mid-point of PQ is

Angle between tangents drawn from the point (1, 4) to the parabola y² = 4x is