A circle with centre $$$C$$$ has equation $$$(x-8)^{2}+(y-4)^{2}=100$$$. Find the $$$x$$$-coordinates of $$$A$$$ and $$$B$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_13 Year：2020 Question No：11(d)

Answer:

$(x-8)^{2}+(7 x-2-4)^{2}=100$ or equivalent in terms of $y$
$50 x^{2}-100 x(=0)$
$x=0$ and 2
Alternative method for question 11(d)
$
\begin{array}{l}
\mathbf{M C}=\left(\begin{array}{c}
7 \\
-1
\end{array}\right) \\
\left(\begin{array}{l}
1 \\
5
\end{array}\right)+\left(\begin{array}{l}
-1 \\
-7
\end{array}\right)=\left(\begin{array}{c}
0 \\
-2
\end{array}\right),\left(\begin{array}{l}
1 \\
5
\end{array}\right)+\left(\begin{array}{l}
1 \\
7
\end{array}\right)=\left(\begin{array}{c}
2 \\
12
\end{array}\right)
\end{array}
$
$x=0$ and 2

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

Answer:

Knowledge points:

Solution:

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