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Question

The length of tangent from the point (1,2) to the circle x2+y28x+5y7=0.

A
1
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B
4
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C
2
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D
6
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Solution

The correct option is B 4
The given equation of the circle can be written as
(x4)2+(y+52)2162547=0
or, (x4)2+(y+52)2=1174
So, centere of the circle is (4,52) and radius is 1172 units.
Now distance between the point (1,2) and (4,52) is 1812 units which is greater than the radius of the circle.
So, the point (1,2) lies outside of the circle.
The length of the tangent from the point (1,2) to the circle x2+y28x+5y7=0 is (1)2+22+8+107=16=4 units.

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