document.write( "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. \n" ); document.write( "

Algebra.Com's Answer #521708 by josgarithmetic(39620) $\"\"$ $\"About$

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$\"y=x%5E2\"$ 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, $\"A%3C0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"Ax%5E2%2BEy=0\"$ is a parabola, \r
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\n" ); document.write( "\n" ); document.write( "Solve for y:
\n" ); document.write( " $\"Ey=-Ax%5E2\"$
\n" ); document.write( " $\"y=-%28A%2FE%29x%5E2\"$
\n" ); document.write( "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. \n" ); document.write( "

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