The equation of a line is $$$y=m x+c$$$, where $$$m$$$ and $$$c$$$ are constants, and the equation of a curve is $$$x y=16$$$. Given that the line is a tangent to the curve, express $$$m$$$ in terms of $$$c$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_11 Year：2020 Question No：5(a)

Answer:

\[
x(m x+c)=16 \rightarrow m x^{2}+c x-16=0
\]
Use of $b^{2}-4 \mathrm{ac}=c^{2}+64 m$
Sets to $0 \rightarrow m=\frac{-c^{2}}{64}$

1.1.2 find the discriminant of a quadratic polynomial and use the discriminant

1.1.4 solve by substitution a pair of simultaneous equations of which one is linear and one is quadratic