Question

What is the standard equation of this hyperbola?
4x^2 = 36 + 9y^2

Answer 1

@Michele_Laino

Answer 2

\[\frac{ x^2 }{ 3^2 }-\frac{ y^2 }{ 5^2}=1\]

Answer 3

Thats how a is set up

Answer 4

we can write this:
\[\Large 4{x^2} - 9{y^2} = 36\]

Answer 5

now I divide both sides by 36, so I get:
\[\Large \frac{{4{x^2}}}{{36}} - \frac{{9{y^2}}}{{36}} = 1\]

Answer 6

please simplify the last equation

Answer 7

what do you get?

Answer 8

\[6 and 4\]

Answer 9

\[\frac{ x^2 }{ 4^2 }-\frac{ y^2 }{ 6^2 }=1\]

Answer 10

@Michele_Laino

Answer 11

hint:
\[\Large \frac{{4{x^2}}}{{36}} - \frac{{9{y^2}}}{{36}} = \frac{{{x^2}}}{{\frac{{36}}{4}}} - \frac{{{y^2}}}{{\frac{{36}}{9}}}\]

Answer 12

so its 2^2 and 3^2

Answer 13

yes! it is:
\[\Large \frac{{4{x^2}}}{{36}} - \frac{{9{y^2}}}{{36}} = \frac{{{x^2}}}{{\frac{{36}}{4}}} - \frac{{{y^2}}}{{\frac{{36}}{9}}} = \frac{{{x^2}}}{{{3^2}}} - \frac{{{y^2}}}{{{2^2}}} = 1\]