Question 161956
{{{5x^2 + 9y^2 = 45}}} Start with the given equation


{{{5(x-0)^2 + 9(y-0)^2 = 45}}} Replace "x" with "x-0" and replace "y" with "y-0". This is valid since adding/subtracting zero doesn't change the equation.



{{{5(x-0)^2/45 + 9(y-0)^2/45 = cross(45/45)}}} Divide EVERY term by 45 to make the right side equal to 1.



{{{(x-0)^2/9 + (y-0)^2/5 = 1}}} Reduce



Take note that {{{3^2=9}}} and {{{(sqrt(5))^2=5}}}



{{{(x-0)^2/(3^2) + (y-0)^2/(sqrt(5))^2 = 1}}} Replace "9" with {{{3^2}}}. Replace "5" with {{{(sqrt(5))^2}}}



Remember, the equation of any ellipse is {{{(x-h)^2/a^2+(y-k)^2/b^2=1}}}. 


Since the equation fits this format where {{{h=0}}}, {{{a=3}}}, {{{k=0}}}, and {{{b=sqrt(5)}}}, this shows us that the equation {{{5x^2 + 9y^2 = 45}}} is an ellipse.


So you are correct. Once again you can use a graph to verify your answer.