A diameter of a circle $$\(C_{1}\)$$ has end-points at $$\((-3,-5)\)$$ and $$\((7,3)\)$$. The circle $$\(C_{1}\)$$ is translated by $$\(\left(\begin{array}{l}8 \\ 4\end{array}\right)\)$$ to give circle $$\(C_{2}\)$$, as shown in the diagram. Find an equation of the circle $$\(C_{2}\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：12(b)
Answer:
Centre \(=\) their \((2,-1)+\left(\begin{array}{l}8 \\
4\end{array}\right)=(10,3)\)
\((x-10)^{2}+(y-3)^{2}=\) their 41
4\end{array}\right)=(10,3)\)
\((x-10)^{2}+(y-3)^{2}=\) their 41
Knowledge points:
1.2.5 understand and use the transformations of the graph of and simple combinations of these. (Including use of the terms ‘translation’, ‘reflection’ and ‘stretch’ in describing transformations. Questions may involve algebraic or trigonometric functions, or other graphs with given features.)
1.3.3 understand that the equation represents the circle with centre and radius (Including use of the expanded form.)
Solution:
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