Tangents, normals and lociEdexcel International A Level Further Maths: Mind map

Exam questions on Tangents, normals and loci

1. The ellipse $E$ has equation $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $P$ is the point $\left(4,\frac95\right)$ on $E$.
   The normal to $E$ at $P$ meets the $x$-axis at $A$. Find the $x$-coordinate of $A$.2 marks
2. The hyperbola $H$ has equation $\frac{x^2}{16}-\frac{y^2}{9}=1$.
   Show that no tangent to $H$ has gradient $\frac12$.2 marks
3. The ellipse $E$ has equation $\frac{x^2}{20}+\frac{y^2}{5}=1$ and $P$ is the point $(2,2)$ on $E$.
   Find an equation of the normal to $E$ at $P$.3 marks