The length of the chord of the parabola y² = 4ax(a > 0) which passes through the vertex and makes an acute angle $$\alpha $$ with the axis of the parabola is

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