The diagram shows a circle with centre $$\(A\)$$ passing through the point $$\(B\)$$. A second circle has centre $$\(B\)$$ and passes through $$\(A\)$$. The tangent at $$\(B\)$$ to the first circle intersects the second circle at $$\(C\)$$ and $$\(D\)$$. The coordinates of $$\(A\)$$ are $$\((-1,4)\)$$ and the coordinates of $$\(B\)$$ are $$\((3,2)\)$$. Find, by calculation, the $$\(x\)$$-coordinates of $$\(C\)$$ and $$\(D\)$$. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_w20_qp_11 Year：2020 Question No：9(c)
Answer:
\((x-3)^{2}+(2 x-6)^{2}=\) their 20
\(5 x^{2}-30 x+25=0\) or \(5(x-3)^{2}=20\)
\([(5)(x-5)(x-1) \quad\) or \(\quad x-3=\pm 2] \quad x=5,1\)
\(5 x^{2}-30 x+25=0\) or \(5(x-3)^{2}=20\)
\([(5)(x-5)(x-1) \quad\) or \(\quad x-3=\pm 2] \quad x=5,1\)
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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