A) (7, -4)
B) (15,-10)
C) (1/7, 8/7)
D) (0, 5/4)
Correct Answer: B
Solution :
Let point\[({{x}_{1}},\,\,{{y}_{1}})\]be on the line\[3x+4y=5\]. \[3{{x}_{1}}+4{{y}_{1}}=5\] ... (i) Also, \[{{({{x}_{1}}-1)}^{2}}+{{({{y}_{1}}-2)}^{2}}\] \[={{({{x}_{1}}-3)}^{2}}+{{({{y}_{1}}-4)}^{2}}\] \[\Rightarrow \] \[x_{1}^{2}+y_{1}^{2}-2{{x}_{1}}-4{{y}_{1}}+5=x_{1}^{2}+y_{1}^{2}-6{{x}_{1}}\] \[-8{{y}_{1}}+25\] \[4{{x}_{1}}+4{{y}_{1}}=20\] ... (ii) On solving Eqs. (i) and (ii), we get \[{{x}_{1}}=15,\,\,{{y}_{1}}=-10\]
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