The equation of a circle is Re ( z ^ 2 ) + 2 (Im(z)) ^ 2 + 2 Re (z)...

We have, $Re \left({z}^{2}\right) + 2{\left(Im \left(z\right)\right)}^{2} + 2 Re \left(z\right) = 0$

where $z = x + iy$

Equation of circle is \left({x}^{2} - {y}^{2}\right) + 2{y}^{2} + 2x = 0$</p><p>${x}^{2} + {y}^{2} + 2x = 0$</p><p>Centre: \left(- 1, 0\right)$

Parabola : ${\left(x - 3\right)}^{2} = y - 4$

Vertex : \left(3, 4\right)$</p><p>Equation of line$≡ y - 0 = \dfrac{4 - 0}{3 + 1}\left(x + 1\right)

$⇒ y = x + 1$

Hence, $y -$ intercept = 1 .