the equation of the parabola whose axis is parallel to y –axis and passing through  is (-3,1), (1,1) is

If 2x + y + a = 0 is a focal chord of the parbola y² + 8x = 0

The locus of the point of intersection of two tangents to the parabola y² = 4ax which make the θ₁ and θ₂ with the axis so that tan θ₁ tanθ₂  = k is

The length of the latus rectum of the parabola 3x² – 9x + 5y – 2 = 0 is

The curve described parametrically by x=t²+t+1, y= t²-t+1 represents

The equation to the parabola having focus (-1,-1) and directrix 2x -3y +6 = 0 is

The angles between tangents to the parabola y² = 4ax at the points where it intersects with the line x – y –a = 0 is

The sum of the slopes of the tangents to the parabola y² = 8x drawn from the point (-2,3) is

The tangent to y² = ax makes an angle 45⁰ with x- axis. Then its point of contact is

Through the vertex O of the parabola y² = 4ax a perpendicular is drawn to any tangent meeting it at P and the parabola at Q.Then OP.OQ =