The problem presents an equation involving $x^2$ and $y^2$: $\frac{-x^2}{9} = \frac{y^2}{4}$. We want to determine the relationship between $x$ and $y$ defined by this equation.

1. Problem Description

The problem presents an equation involving $x^2$ and $y^2$: $\frac{-x^2}{9} = \frac{y^2}{4}$. We want to determine the relationship between $x$ and $y$ defined by this equation.

2. Solution Steps

We start with the given equation:

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

Multiply both sides by 36 to eliminate the fractions:

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

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

Add $4x^2$ to both sides:

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

Since $x^2$ and $y^2$ are always non-negative, $4x^2 \geq 0$ and $9y^2 \geq 0$. The only way for the sum of two non-negative terms to be zero is if both terms are zero. Therefore, we must have $4x^2 = 0$ and $9y^2 = 0$.

This implies $x^2 = 0$ and $y^2 = 0$.

Taking the square root of both equations gives $x=0$ and $y=0$.

3. Final Answer

The solution to the equation $\frac{-x^2}{9} = \frac{y^2}{4}$ is $x=0$ and $y=0$. In other words, the only solution is the point (0,0).