L1>L2
L1<L2
L1L2=√2
L1=L2
The given curves are x² + y² = 9 and y² = 8x. To find the points of intersection, let us substitute the values of y².
x² + 8x − 9 = 0
(x + 9)(x − 1) = 0
x = −9 is not possible.
Hence, x = 1
y² = 8 ⇒ y = ±2√2
The two points are (1, 2√2) and (1, −2√2)
L1 = 2 × 2√2 = 4√2
L2 = 4a = 8 (where a is the distance from the vertex to the focus in the parabola y² = 4ax)
Hence, L2 > L1