Question 969407
start with 9x^2 + y^2 - 27 = 0
add 27 to both sides of the equation to get:
9x^2 + y^2 = 27
divide both sides of the equation by 27 to get:
9x^2 / 27 + y^2 / 27 = 1
simplify to get x^2/3 + y^2 / 27 = 1
that's in the standard form of the equation of a vertically oriented ellipse, which is (x-h)^2 / b^2 + (y-k)^2 / a^2 = 1
(h,k) is the vertex.
the graph of the equation is shown below:
{{{graph(600,600,-15,15,-15,15,sqrt(27-9x^2),-sqrt(27-9x^2))}}}
here's a reference that explains it all.
<a href = "http://www.purplemath.com/modules/ellipse.htm" target = "_blank">http://www.purplemath.com/modules/ellipse.htm</a>