1.5.14 Convert between cartesian and parametric forms (A-level only)

A curve $C\,$ has parametric equations

\tan t, \quad y = 2\sec^2 t - 3, \quad 0 \leq t \leq 2\pi, \, t \neq \frac{\pi}{2}, \frac{3\pi}{2}

a.

Find an equation for $C\,$ in the form $y = f (x)$ and state the domain for which the curve is defined.

[3]

b.

Sketch the curve $C$ .

[3]

A curve $C\,$ has parametric equations

\tan t, \quad y = 2\sec^2 t - 3, \quad 0 \leq t \leq 2\pi, \, t \neq \frac{\pi}{2}, \frac{3\pi}{2}

a.

Find an equation for $C\,$ in the form $y = f (x)$ and state the domain for which the curve is defined.

[3]

b.

Sketch the curve $C$ .

[3]

1.5.14 Convert between cartesian and parametric forms (A-level only) Questions