A) (0, 0), (a, b)
B) (0, 0), \[\left( \frac{2a{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}},\frac{2b{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}} \right)\]
C) (0, 0), \[\left( \frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}},\frac{{{a}^{2}}+{{b}^{2}}}{{{b}^{2}}} \right)\]
D) None of the above
Correct Answer: B
Solution :
Given circles are \[{{x}^{2}}+{{y}^{2}}=2ax\] ?..(i) and \[{{x}^{2}}+{{y}^{2}}=2by\] ?..(ii) (i) ? (ii) Þ \[0=2(ax-by)\] Þ \[y=\frac{a}{b}x\] From (i), \[{{x}^{2}}+\frac{{{a}^{2}}}{{{b}^{2}}}{{x}^{2}}=2ax\] Þ \[x\left\{ \left( 1+\frac{{{a}^{2}}}{{{b}^{2}}} \right)x-2a \right\}=0\] Þ \[x=0,\ \frac{2a{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\] For \[x=0\], \[y=0\] and for \[x=\frac{2a{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\], \[y=\frac{2{{a}^{2}}b}{{{a}^{2}}+{{b}^{2}}}\] \ The points of intersection are (0, 0) and \[\left( \frac{2a{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}},\ \frac{2{{a}^{2}}b}{{{a}^{2}}+{{b}^{2}}} \right)\].
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