A) \[{{x}^{2}}+{{y}^{2}}+4x-10y+25=0\]
B) \[{{x}^{2}}+{{y}^{2}}-4x-10y+25=0\]
C) \[{{x}^{2}}+{{y}^{2}}-4x-10y+16=0\]
D) \[{{x}^{2}}+{{y}^{2}}-14y+8=0\]
Correct Answer: B
Solution :
First find the centre. Let centre 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 (i), we get \[-4h-6k+8h+10k=16+25-4-9\] or \[4h+4k-28=0\] or \[h+k-7=0\] ?.(iii) From (iii) and (ii), we get (h, k) as (2, 5). Hence centre is (2, 5) and radius is 2. Now find the equation of circle. Trick : Obviously, circle \[{{x}^{2}}+{{y}^{2}}-4x-10y+25=0\] passes through (2, 3) and (4, 5).
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