A diameter of a circle $$\(C_{1}\)$$ has end-points at $$\((-3,-5)\)$$ and $$\((7,3)\)$$. Hence show that the $$\(x\)$$-coordinates of $$\(R\)$$ and $$\(S\)$$ satisfy the equation $$\(5 x^{2}-60 x+159=0\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_m20_qp_12 Year：2020 Question No：12(d)
Answer:
\((x-10)^{2}+(-2 x+13-3)^{2}=41\)
\(x^{2}-20 x+100+4 x^{2}-40 x+100=41 \rightarrow 5 x^{2}-60 x+159=0\)
\(x^{2}-20 x+100+4 x^{2}-40 x+100=41 \rightarrow 5 x^{2}-60 x+159=0\)
Knowledge points:
1.3.4 use algebraic methods to solve problems involving lines and circles (Including use of elementary geometrical properties of circles, e.g. tangent perpendicular to radius, angle in a semicircle, symmetry.) (Implicit differentiation is not included.)
1.3.5 understand the relationship between a graph and its associated algebraic equation, and use the relationship between points of intersection of graphs and solutions of equations. (e.g. to determine the set of values of for which the line intersects, touches or does not meet a quadratic curve.)
Solution:
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