Quick questions on Parametric equations: parametric curves, conversion to Cartesian form and parametric differentiation - CCEA A-Level Mathematics

To find the Cartesian equation, eliminate the parameter. If the parameter is easy to make the subject (for example $t = \frac{y}{2}$), substitute it into the other equation. For trigonometric parameters, use an identity such as $\sin^2\theta + \cos^2\theta = 1$ to eliminate $\theta$, which often produces a circle or an ellipse. Sometimes the parameter appears in both equations in a way that needs a little manipulation first, such as squaring one equation or adding the two, before the identity can be applied; the goal is always a single equation relating $x$ and $y$ with no parameter left.

A curve has $x = t + 1$, $y = t^2$. Find the Cartesian equation. [2 marks]

For $x = t^3$, $y = t^2$, find $\frac{dy}{dx}$ in terms of $t$. [2 marks]

What identity eliminates $\theta$ from $x = \cos\theta$, $y = \sin\theta$? [1 mark]