A) 1
B) 2
C) 3
D) 4
Correct Answer: B
Solution :
The equations of circles are \[{{x}^{2}}+\text{ }{{y}^{2}}-\text{ }8x+2y=0\] \[{{x}^{2}}+\text{ }{{y}^{2}}-2x-16y+25=0.\] The centre and radius of first circle are\[{{C}_{1}}(4,-1)\] and \[\sqrt{17}\]respectively. Also, the centre and radius of second circle are \[{{C}_{2}}(1,8)\] and\[\sqrt{40}\] respectively. Now, \[{{C}_{1}}{{C}_{2}}=\sqrt{{{(1-4)}^{2}}+{{(8+1)}^{2}}}\] \[=\sqrt{9+81}=\sqrt{90}\] and \[{{r}_{1}}+{{r}_{2}}=\sqrt{17}+\sqrt{40}\] \[\therefore \]These two circles intersect each other. Hence, the number of common tangents are 2.
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