If the parabola y² = 4ax passes through the point (3, 2), then the length of its latus rectum is

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

If the focus of a parabola is (0, –3) and its directrix is y = 3, then its equation is

If the vertex of the parabola is the point (–3, 0) and the directrix is the line x + 5 = 0, then its equation is

The equation of the ellipse whose focus is (1, –1), the directrix the line x – y – 3 = 0 and eccentricity is