A) \[{{x}^{2}}+{{y}^{2}}+4x-10y+25=0\]
B) \[{{x}^{2}}+{{y}^{2}}-4x-10y+16=0\]
C) \[{{x}^{2}}+{{y}^{2}}-4x-10y+25=0\]
D) None of the above
Correct Answer: C
Solution :
Let the centre of circle be (h, k). Then \[\sqrt{{{(h-2)}^{2}}+{{(k-3)}^{2}}}\] \[=\sqrt{{{(h-4)}^{2}}+{{(k-5)}^{2}}}\] ... (i) and \[k-4h+3=0\] ... (ii) From Eq. (i) \[-4h-6k+8h+10k=16+25-4-9\] \[\Rightarrow \] \[h+k-7=0\] ? (iii) On solving Eqs. (ii) and (iii), we get the centre of circle (2, 5). Now, radius\[=\sqrt{{{(2-2)}^{2}}+{{(5-3)}^{2}}}=2\] \[\therefore \]Required equation of circle is \[{{(x-2)}^{2}}+{{(y-5)}^{2}}={{2}^{2}}\] \[\Rightarrow \] \[{{x}^{2}}+{{y}^{2}}-4x-10y+25=0\]
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