put into standard form for that particular shape. 9x^2+4y^2=36

Question

mathmale · Answer

First, do you recognize which conic section corresponds to this equation?  It's not a cone, and not a parabola.  What is it?

gabrielah96 · Answer

How can you tell?

mathmale · Answer

We need to be able to write out and recognize the most basic equations of the four conic sections:  ellipse, hyperbola, circle and parabola.

In this case we know we don't have a circle because the coefficients of x^2 and y^2 are different in the expression you've typed in.  In the case of a circle, the coeff. would be equal.

There's more to it.  But here you have an ellipse.  

Write out the given equation and divide every term by 36.  simplify the result.

gabrielah96 · Answer

so is it 1x^2/4^2+1y^2/9^2=1 ?

mathmale · Answer

$$\frac{ x^2 }{ 2^2 }+\frac{ y^2 }{ 3^2 }=1$$

mathmale · Answer

Yes, this is different from yours.  Why?

gabrielah96 · Answer

i didnt simplify it

mathmale · Answer

In the first term of the given equation, you have 9x^2, which you divided by 36.  the result was$$\frac{ 9x^2 }{ 36 }=\frac{ x^2 }{ 4 }$$   and that 4 is the same as 2^2.  ok?

mathmale · Answer

Yes, and so we end up with $$\frac{ x^2 }{ 2^2 }+\frac{ y^2 }{ 3^2 }=1$$ which is the equation of our ellipse in std. form.