The equation of a circle is Re z 2 + 2 Im z 2 + 2 Re z = 0 , where z = x + i y . A line which passes through the centre of the given circle and the vertex of the parabola, x 2 - 6 x - y + 13 = 0 , has y -intercept equal to _________.

Step-by-step solution

We have, Re z 2 + 2 Im z 2 + 2 Re z = 0 where z = x + i y Equation of circle is x 2 - y 2 + 2 y 2 + 2 x = 0 x 2 + y 2 + 2 x = 0 Centre: - 1 , 0 Parabola : x - 3 2 = y - 4 Vertex : 3 , 4 Equation of line ≡ y - 0 = 4 - 0 3 + 1 x + 1 ⇒ y = x + 1 Hence, y - intercept = 1 .