A circle with centre $$\(C\)$$ has equation $$\((x-8)^{2}+(y-4)^{2}=100\)$$. Find the $$\(x\)$$-coordinates of $$\(A\)$$ and $$\(B\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
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 \(y\)
\[
50 x^{2}-100 x(=0)
\]
\[
x=0 \text { and } 2
\]
Alternative method for question 11(d)
\[
\mathbf{M C}=\left(\begin{array}{c}
7
-1
\end{array}\right)
\]
\[
\left(\begin{array}{l}
1
5
\end{array}\right)+\left(\begin{array}{l}
-1
-7
\end{array}\right)=\left(\begin{array}{c}
0
-2
\end{array}\right),\left(\begin{array}{l}
1
5
\end{array}\right)+\left(\begin{array}{l}
1
7
\end{array}\right)=\left(\begin{array}{c}
2
12
\end{array}\right)
\]
\(x=0\) and 2
\[
50 x^{2}-100 x(=0)
\]
\[
x=0 \text { and } 2
\]
Alternative method for question 11(d)
\[
\mathbf{M C}=\left(\begin{array}{c}
7
-1
\end{array}\right)
\]
\[
\left(\begin{array}{l}
1
5
\end{array}\right)+\left(\begin{array}{l}
-1
-7
\end{array}\right)=\left(\begin{array}{c}
0
-2
\end{array}\right),\left(\begin{array}{l}
1
5
\end{array}\right)+\left(\begin{array}{l}
1
7
\end{array}\right)=\left(\begin{array}{c}
2
12
\end{array}\right)
\]
\(x=0\) 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
Solution:
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