1. Write the relation between \(x\) and \(y\) by eliminating \(\theta\) from the equations \(2x = 3\sin\theta\) and \(5y = 3\cos\theta\).

2. Given: \(x = a \sec \theta\), \(y = b \tan \theta\); eliminate \(\theta\) and establish a relation between \(x\) and \(y\).

3. Given: \[ x \cos \theta = 3 \quad \text{and} \quad 4 \tan \theta = y \] Find the relation between \(x\) and \(y\) eliminating \(\theta\).

4. \(x \propto y^2\) and \(y = 2a\). When \(y = a\), determine the relationship between \(x\) and \(y\).

(a) \(y^2 = 4ax \) (b) \(x^2 = 4ay \) (c) \(x=y\) (d) \(x^2 = 2ay\)

5. \(x \propto y^2\) and \(y = 2a\). When \(y = a\), determine the relationship between \(x\) and \(y\).

6. \(x \propto y^2\), and \(y = 2a\) when \(x = a\). Determine the relationship between \(x\) and \(y\).