Tangents and normalsAQA A-Level Maths: Mind map

Exam questions on Tangents and normals

1. The curve $C$ has equation $y=2x^3-5x+1$ and passes through the point $P$ where $x=2$.
   Find the equation of the normal to $C$ at $P$, giving your answer in the form $ax+by+c=0$ where $a$, $b$ and $c$ are integers.2 marks
2. The curve $C$ has equation $y=x+\frac{12}{x}$ for $x\neq0$ and passes through the point $P(3,7)$.
   Find the coordinates of the other point on $C$ at which the tangent is parallel to the tangent at $P$.2 marks
3. The curve $C$ has equation $y=x^2+px+q$, where $p$ and $q$ are constants. The tangent to $C$ at the point $(1,2)$ has gradient $5$.
   Find the values of $p$ and $q$.3 marks