The flight path of a surveillance drone in a vertical cross-section is modelled by the parametric equations

2t^2 - 16t, \quad y = t^3 - 16t, \quad t \in \mathbb{R}

where $x\,$ represents the horizontal displacement from a control tower and $y\,$ represents the height relative to a safety baseline. The drone's path crosses the baseline at the origin and at the points $A\,$ and $B$ , where $A\,$ and $B\,$ are distinct points.

Find the coordinates of $A\,$ and show that $B\,$ has coordinates $(96, 0)$ .

Show that the equation of the tangent to the path at $B\,$ is

x + y - 96 = 0

The tangent to the path at $B\,$ intersects the path again at the point $P$ .

Find, using algebraic methods, the horizontal displacement of the drone at point $P$ .

The flight path of a surveillance drone in a vertical cross-section is modelled by the parametric equations

2t^2 - 16t, \quad y = t^3 - 16t, \quad t \in \mathbb{R}

Find the coordinates of $A\,$ and show that $B\,$ has coordinates $(96, 0)$ .

Show that the equation of the tangent to the path at $B\,$ is

x + y - 96 = 0

The tangent to the path at $B\,$ intersects the path again at the point $P$ .

Find, using algebraic methods, the horizontal displacement of the drone at point $P$ .

1.5.16 Gradient of a parametric curve (A-level only)

Question 11

Markscheme

1.5.16 Gradient of a parametric curve (A-level only)

Question 11

Markscheme

1.5.16 Gradient of a parametric curve (A-level only)

Question 11

1.5.16 Gradient of a parametric curve (A-level only) Questions

1.5.16 Gradient of a parametric curve (A-level only)

Question 11

1.5.16 Gradient of a parametric curve (A-level only) Questions