Question 8 - A-Level Maths

Exam Board	OCR
Module	C4 (Core Mathematics 4)
Year	2012
Session	June
Topic	Implicit equations and differentiation

Find the gradient of the curve $x ^ { 2 } + x y + y ^ { 2 } = 3$ at the point $( - 1 , - 1 )$.
A curve $C$ has parametric equations $$x = 2 t ^ { 2 } - 1 , y = t ^ { 3 } + t$$
1. Find the coordinates of the point on $C$ at which the tangent is parallel to the $y$-axis.
2. Find the values of $t$ for which $x$ and $y$ have the same rate of change with respect to $t$.