The Angle Between The Tangents Drawn From The Origin To The Parabola y2 = 4a(x – A) 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

Consider the two curves C₁ : y² = 4x, C₂ : x² + y² – 6x + 1 = 0. Then,

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

The equation of the common tangent touching the circle (x – 3)² + y² = 9 and the parabola y² = 4x above the x-axis is