The ratio of latus rectum of given parabola and that of made by locus of point $P$ is:
Step-by-Step Solution
Key Concept: The latus rectum of a parabola $y^2 = 4ax$ has length $4a$, which depends only on the parameter $a$.
For the parabola $y^2 = 8x$, the latus rectum has length $4a = 8$. For the parabola $y^2 = 2(x-6)$, the latus rectum has length $4 \cdot \frac{1}{2} = 2$. Therefore, the ratio of latus rectums is $8:2 = 4:1$.
Correct Answer: 1