The rectangular hyperbolaEdexcel International A Level Further Maths: Mind map

Exam questions on The rectangular hyperbola

1. A rectangular hyperbola $H$ has equation $xy=36$.
   The point $Q$ lies on $H$ and has $x$-coordinate $-9$. Find the value of $t$ at $Q$ and the $y$-coordinate of $Q$.2 marks
2. A curve $C$ has parametric equations $x=5t$, $y=\frac{5}{t}$, where $t\neq0$.
   Find the coordinates of the points where $C$ meets the line $y=x$.2 marks
3. The rectangular hyperbola $H$ has parametric equations $x=2t$, $y=\frac{2}{t}$, $t\neq0$. The point $A$ has parameter $t=a$ and the point $B$ has parameter $t=2a$, where $a>0$.
   Write down the coordinates of $A$ and $B$ in terms of $a$, and hence show that the gradient of the chord $AB$ is $-\frac{1}{2a^2}$.3 marks