(x^(2))/(9)-(y^(2))/(4)=1

Identify Equation Type: Identify the type of equation. The given equation (x^(2))/(9)-(y^(2))/(4)=1 is in the form of a hyperbola equation.Rewrite in Standard Form: Rewrite the equation in standard form. The standard form of a hyperbola equation is (x^2)/(a^2) - (y^2)/(b^2) = 1 where a and b are real numbers.Compare with Standard Form: Compare the given equation with the standard form. In the given equation (x^(2))/(9)-(y^(2))/(4)=1, we can see that a^2 = 9 and b^2 = 4.Find Values of a and b: Find the values of a and b. Taking square roots, we get a = 3 and b = 2.Write Final Standard Form: Write the final standard form of the equation. The standard form of the given equation is (x^2)/(3^2) - (y^2)/(2^2) = 1.

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$4$ . $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$

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\frac{x^{2}}{9}-\frac{y^{2}}{4}=1

Identify Equation Type: Identify the type of equation. $\newline$ The given equation $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$ is in the form of a hyperbola equation.
Rewrite in Standard Form: Rewrite the equation in standard form. $\newline$ The standard form of a hyperbola equation is $(\frac{x^2}{a^2}) - (\frac{y^2}{b^2}) = 1$ where $a$ and $b$ are real numbers.
Compare with Standard Form: Compare the given equation with the standard form. $\newline$ In the given equation $(\frac{x^{2}}{9})-(\frac{y^{2}}{4})=1$ , we can see that $a^{2} = 9$ and $b^{2} = 4$ .
Find Values of $a$ and $b$ : Find the values of $a$ and $b$ . Taking square roots, we get $a = 3$ and $b = 2$ .
Write Final Standard Form: Write the final standard form of the equation. $\newline$ The standard form of the given equation is (\frac{x^$2$}{$3$^$2$} - \frac{y^$2$}{$2$^$2$} = \(1)\.