What type of conic section has the equation $9 x^{2} - 4 y^{2} = 36$ $9x^2-4y^2=36$ ?

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Answer 1 · 2014-09-25T01:46:04

This equation is almost in the form that we need to easily graph and identify.

$9 x^{2} - 4 y^{2} = 36$ $9x^2-4y^2=36$

Divide all terms by 36.

$\frac{9 x^{2}}{36} - \frac{4 y^{2}}{36} = \frac{36}{36}$ $(9x^2)/36-(4y^2)/36=36/36$

Simplify

$\frac{x^{2}}{4} - \frac{y^{2}}{9} = 1$ $(x^2)/4-(y^2)/9=1$

Be more explicit with the numerator of each term.

$\frac{{(x - 0)}^{2}}{4} - \frac{{(y - 0)}^{2}}{9} = 1 \Rightarrow H y p e r b o l a$ $((x-0)^2)/4-((y-0)^2)/9=1=> Hyperbola$

What type of conic section has the equation 9x^2-4y^2=369x2−4y2=369x^2-4y^2=36?