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

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) (Show Source): You can put this solution on YOUR website!
is an equation of a parabola. If instead this is also a parabola but although same vertex, flipped upside down. The first case, , and in second case, .

is a parabola,

Solve for y:

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.
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