SOLUTION: derive the equation of the parabola with its focus at (-2, -1) and whose latus rectum joins the points (-2, 2) and (-2, -4)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: derive the equation of the parabola with its focus at (-2, -1) and whose latus rectum joins the points (-2, 2) and (-2, -4)       Log On


   

Question 1044922: derive the equation of the parabola with its focus at (-2, -1) and whose latus rectum joins the points (-2, 2) and (-2, -4)

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use a form, 4p%28x-h%29=%28y-k%29%5E2, because if you had been given directrix as well as focus, you would be able to judge that the parabola has horizontal symmetry axis and will give the shown equational form. You do not yet know if directrix is to the left or to the right of your focus.

Your focus and latus rectum are enough to tell you that SYMMETRY AXIS is y=-1. This means you can revise the parabola equation to 4p%28x-h%29=%28y%2B1%29%5E2.


FINDING p AND h

Your two latus rectum endpoints will give you two more specific equations to form a system in the TWO unknown variables, p and h. Form and simplify those equations, and solve that system.
(How can you be sure if p is positive or negative?)