SOLUTION: Find the equation of a parabola with vertex on the line y = x + 2, axis parallel to Oy, latus rectum 6 and passing through ( -3, -1).

Algebra ->  Finance -> SOLUTION: Find the equation of a parabola with vertex on the line y = x + 2, axis parallel to Oy, latus rectum 6 and passing through ( -3, -1).      Log On


   

Question 1190857: Find the equation of a parabola with vertex on the line y = x + 2, axis parallel to Oy, latus rectum 6 and passing through ( -3, -1).
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

There is more than one solution.
Note that (-3,-1) is on the line y=x%2B2:
-1=-3%2B2
-1=-1->true
so the vertex can be (-3,-1).
It doesn’t have to be there, but that is an easy solution.
use vertex formula
y+=+a%28x-h%29%5E2%2Bk
Length of latus rectum is 6, so the leading coefficient is ±1%2F6
substitute the coordinates the vertex and the leading coefficient
y+=+%281%2F6%29%28x%2B3%29%5E2-1+
or
y+=+-%281%2F6%29%28x%2B3%29%5E2-1

graph: y+=+%281%2F6%29%28x%2B3%29%5E2-1+


graph: y+=+-%281%2F6%29%28x%2B3%29%5E2-1+