The equation of a circle is Re(z^2)+2[Im(z)]^2+2Re(z)=0 where z=x+iy.

Question

The equation of a circle is $	ext{Re}(z^2)+2[	ext{Im}(z)]^2+2	ext{Re}(z)=0$ where $z=x+iy$. A line which passes through the centre of the given circle and the vertex of the parabola $x^2-6x-y+13=0$ has $y$-intercept equal to ........

Answer: 1

Accepted Answer

$	ext{Re}(z^2)=x^2-y^2$; the circle equation becomes $x^2-y^2+2y^2+2x=0\Rightarrow x^2+y^2+2x=0$, centre $(-1,0)$.

Parabola: $y=(x-3)^2+4$, vertex $(3,4)$.

Line through $(-1,0)$ and $(3,4)$: slope $=1$, $y=x+1$ --- $y$-intercept $=1$.

Solutions · 1