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 instead that $$$m=-4$$$, find the set of values of $$$c$$$ for which the line intersects the curve at two distinct points. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

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

Answer:

\[
x(-4 x+c)=16
\]
Use of $b^{2}-4 \mathrm{ac} \rightarrow c^{2}-256$
$c>16$ and $c<-16$

Knowledge points:

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

1.1.3 solve quadratic equations, and quadratic inequalities, in one unknown (By factorising, completing the square and using the formula.)

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

1.3.5 understand the relationship between a graph and its associated algebraic equation, and use the relationship between points of intersection of graphs and solutions of equations. (e.g. to determine the set of values of for which the line intersects, touches or does not meet a quadratic curve.)

Answer:

Knowledge points:

Solution:

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