The diagram shows part of the curve $$$y=\frac{8}{x+2}$$$ and the line $$$2 y+x=8$$$, intersecting at points $$$A$$$ and $$$B$$$. The point $$$C$$$ lies on the curve and the tangent to the curve at $$$C$$$ is parallel to $$$A B$$$. Find, by calculation, the coordinates of $$$A, B$$$ and $$$C$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_11 Year：2020 Question No：11(a)

Answer:

Simultaneous equations $\frac{8}{x+2}=4-1 / 2 x$
$x=0$ or $x=6 \rightarrow A(0,4)$ and $B(6,1)$
At $C \frac{-8}{(x+2)^{2}}=-\frac{1}{2} \rightarrow C(2,2)$
(B1 for the differentiation. M1 for equating and solving)

Knowledge points:

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

1.7.3 apply differentiation to gradients, tangents and normals, increasing and decreasing functions and rates of change (Including connected rates of change, e.g. given the rate of increase of the radius of a circle, find the rate of increase of the area for a specific value of one of the variables.)

Answer:

Knowledge points:

Solution:

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