SOLUTION: Show than an equation of the form Ax^2+Ey=0, A doesn't equal 0, E doesn't equal ), is the equation of a parabola with vertex at (0,0), and axis of symmetry the y-axis. Find its foc

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Show than an equation of the form Ax^2+Ey=0, A doesn't equal 0, E doesn't equal ), is the equation of a parabola with vertex at (0,0), and axis of symmetry the y-axis. Find its foc      Log On


   

Question 865445: Show than an equation of the form Ax^2+Ey=0, A doesn't equal 0, E doesn't equal ), is the equation of a parabola with vertex at (0,0), and axis of symmetry the y-axis. Find its focus and directrix. Assume that A>0 and E<0.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
y=x%5E2 is an equation of a parabola. If instead y=-x%5E2 this is also a parabola but although same vertex, flipped upside down. The first case, A%3E0, and in second case, A%3C0.

Ax%5E2%2BEy=0 is a parabola,

Solve for y:
Ey=-Ax%5E2
y=-%28A%2FE%29x%5E2
No horizontal translation is applied to x; and no vertical translation is applied to y; so the vertex is still (0,0). Vertical stretch or shrink will be different depending on ratio A/E. Axis of symmetry is the same as for y=x^2, because position of the given equation is untranslated from standard, so the same x=0 axis of symmetry.