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

A curve has the parametric equations

3\cos t, \quad y = \sec^2 t, \quad 0 < t < \frac{\pi}{2}

Find an expression for $dydx\displaystyle \frac{dy}{dx}$ in terms of $t$ .

[3]

Find an equation of the tangent to the curve when $t=π4\displaystyle t = \frac{\pi}{4}$ .

[5]

Find a cartesian equation for the curve.

[4]

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

A curve has the parametric equations

3\cos t, \quad y = \sec^2 t, \quad 0 < t < \frac{\pi}{2}

Find an expression for $dydx\displaystyle \frac{dy}{dx}$ in terms of $t$ .

[3]

Find an equation of the tangent to the curve when $t=π4\displaystyle t = \frac{\pi}{4}$ .

[5]

Find a cartesian equation for the curve.

[4]