The problem is to find the solutions for the equation $ - \frac{x^2}{9} = \frac{y^2}{4} $.

1. Problem Description

The problem is to find the solutions for the equation $- \frac{x^2}{9} = \frac{y^2}{4}$.

2. Solution Steps

We want to find the solutions to the equation $- \frac{x^2}{9} = \frac{y^2}{4}$.

First, we can multiply both sides of the equation by $36$ to eliminate the fractions:

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

$- 4x^2 = 9y^2$

Now we can add $4x^2$ to both sides to get:

$0 = 4x^2 + 9y^2$

$4x^2 + 9y^2 = 0$

Since $x^2$ and $y^2$ are non-negative, $4x^2$ and $9y^2$ are also non-negative. The sum of two non-negative terms can only be zero if both terms are zero. Therefore, we must have:

$4x^2 = 0$ and $9y^2 = 0$

$x^2 = 0$ and $y^2 = 0$

$x = 0$ and $y = 0$

Therefore, the only solution to the equation is $x = 0$ and $y = 0$.

3. Final Answer

$x = 0, y = 0$