3.5.4 Differentiation (A-level only)

A particle moves in a 2D plane such that its position is constrained by the curve with equation

2(x - 2y)^2 = 5x + 3y + 12

The curve intersects the positive $x$ -axis at the point $P$ .

Show that the gradient of the curve at $P$ is $1135\frac{11}{35}$ .

[4]

Find an equation for the normal to the curve at $P$ , giving your answer in the form $a x + b y = c$ , where $a$ , $b$ and $c$ are integers.

[3]

3.5.4 Differentiation (A-level only) Questions

A particle moves in a 2D plane such that its position is constrained by the curve with equation

2(x - 2y)^2 = 5x + 3y + 12

The curve intersects the positive $x$ -axis at the point $P$ .

Show that the gradient of the curve at $P$ is $1135\frac{11}{35}$ .

[4]

Find an equation for the normal to the curve at $P$ , giving your answer in the form $a x + b y = c$ , where $a$ , $b$ and $c$ are integers.

[3]