The ratio of latus rectum of given parabola and that of made by locus of point $P$ is:
Step-by-Step Solution
Key Concept: For a parabola y² = 4ax, the latus rectum length is 4a. The given parabola y² = 8x has a = 2 (latus rectum = 8), while the locus parabola y² = 2(x-6) has a = 1/2 (latus rectum = 2), yielding a 4:1 ratio.
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