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Find the radius and centre of the circle...

Find the radius and centre of the circle of the circle `x^(2) + y^(2) + 2x + 4y -1=0`.

A

`sqrt(6)` and `(-1,-2)`

B

`sqrt(2)` and `(1,2)`

C

`sqrt(7)` and `(-1,-3)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Equation of circle
`x^(2)+y^(2)+2x+4y-1=0`
Comparing with the general equation of the circle
`x^(2) + y^(2) +2gx + 2fy +c = 0`
`2g = 2,2f =4 and c = -1`
`rArr g = 1, f=2 and c = -1`
`:.` Radius of circle `= sqrt(g^(2)+f^(2)-c)`
`= sqrt((1)^(2)+(2)^(2)-(-1))`
`sqrt(1+4+1)`
`=sqrt(6)` units
And centre of circle `=(-g,-f)=(-1,-2)`.
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