A circle passes through $$\(A\)$$ and $$\(B\)$$ and its centre lies on the line $$\(12 x-5 y=70\)$$. Find an equation of the circle. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................
Exam No：9709_s20_qp_13 Year：2020 Question No：10(b)
Answer:
Solve simultaneously \(12 x-5 y=70\) and their \(3 x+2 y=11\)
\(x=5, y=-2\)
Attempt to find distance between their \((5,-2)\) and either \((-7,3)\) or \((5,11)\)
\((r)=\sqrt{12^{2}+5^{2}}\) or \(\sqrt{13^{2}+0}=13\)
Equation of circle is \((x-5)^{2}+(y+2)^{2}=169\)
\(x=5, y=-2\)
Attempt to find distance between their \((5,-2)\) and either \((-7,3)\) or \((5,11)\)
\((r)=\sqrt{12^{2}+5^{2}}\) or \(\sqrt{13^{2}+0}=13\)
Equation of circle is \((x-5)^{2}+(y+2)^{2}=169\)
Knowledge points:
1.3.3 understand that the equation represents the circle with centre and radius (Including use of the expanded form.)
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.)
Solution:
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