The extreme points of the latus rectum of a parabola are `(7, 5)` and `(7, 3)`. Find the equation of the parabola and the points where it meets the coordinate axes.

Explanation

Focus of the parabola is the mid-point of the latus rectum.
`!` S is (7, 4).
Also axis of the parabola is perpendicular to the latus rectum and passes through the focus. Its equation is
`y-4=0/(5-3)(x-7)`
`!y=4`
Length of the latus rectum
= `(5 - 3) = 2`
Hence the vertex of the parabola is at a distance
2/4=0.5
from the focus. We have two parabolas, one concave rightward and the other concave leftward.
The vertex of the first parabola is (6.5, 4) and its equation is `(y - 4)2 = 2(x - 6.5)` and it meets the x-axis at (14.5, 0). The equation of the second parabola is `(y – 4)^(2) = –2(x - 7.5)`. It meets the x-axis at `(-0.5, 0)`.