Tangents and normals to the parabola and rectangular hyperbolaEdexcel International A Level Further Maths: Mind map

Exam questions on Tangents and normals to the parabola and rectangular hyperbola

1. The parabola $P$ has equation $y^2=12x$.
   Find the equation of the tangent to $P$ at the point $(12,12)$.2 marks
2. The rectangular hyperbola $H$ has equation $xy=24$ and passes through the point $A(4,6)$.
   Find the equation of the normal to $H$ at $A$, in the form $ax+by+c=0$ where $a$, $b$ and $c$ are integers.2 marks
3. The parabola $C$ has equation $y^2=8x$. The point $P$ lies on $C$, has $x$-coordinate 8 and has positive $y$-coordinate.
   Find the equation of the tangent to $C$ at $P$.3 marks