The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12. Then, the length of the latusrectum is

If the line y = x is a tangent to the parabola y = ax² + bx + c at the point (1, 1) and the curve passes through ($$ - $$1, 0), then

Number of common tangents of y = x² and y = $$-$$x² + 4x $$-$$ 4 is

Let P(at², 2at), Q, R(ar², 2ar) be three points on a parabola y² = 4ax. If PQ is the focal chord and PK, QR are parallel where the co-ordinates of K is (2a, 0), then the value of r is