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The number of common tangents of the circles \mathrm{x^2+y^2-2 x-1=0} and \mathrm{x^2+y^2-2 y-7=0} is

Option: 1

2


Option: 2

1


Option: 3

3


Option: 4

4


Answers (1)

best_answer

\mathrm{\text { Centre of } 1^{\text {st }} \text { circle }=(1,0) \text {, radius }=\sqrt{1+0+1}=\sqrt{2}}

Centre of 2nd circle = (0, 1), radius\mathrm{=\sqrt{0+1+7}=2 \sqrt{2}} Distance between centres of two circles

\mathrm{=\sqrt{(1-0)^2+(0-1)^2}=\sqrt{2}}

\mathrm{\text { Difference of radii }=2 \sqrt{2}-\sqrt{2}=\sqrt{2}=\text { distance between centres}}One circle touches internally to other circle, so there is only one common tangent to both.

Posted by

Irshad Anwar

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