Let the latus rectum of the parabola y^2=4x be the common chord to the circles C_1 and C_2…

Question

Let the latus rectum of the parabola $y^2=4x$ be the common chord to the circles $C_1$ and $C_2$, each of them having radius $2\sqrt5$. Then, the distance between the centres of the circles $C_1$ and $C_2$ is:

Accepted Answer

Latus rectum: $x=1$, from $(1,2)$ to $(1,-2)$, half-length $2$.

$$d=\sqrt{r^2-2^2}=\sqrt{20-4}=4.$$

Centres lie on the axis, symmetric about $x=1$: at $(1\pm4,0)$, distance apart $=8$.

Solutions · 1