Find the radius of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$

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Solution

The radius of the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ is $\sqrt{g^{2} + f^{2} - c}$ .

The equation of the circle given $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$

$\Rightarrow g = - 1 f = 2 a n d c = 11$

$\Rightarrow r = \sqrt{(- 1)^{2} + (2)^{2} - (- 11)}$

= $\sqrt{1 + 4 + 11}$

= $\sqrt{16}$

=4

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Find the radius of the circle x2 + y2 − 2x + 4y − 11 = 0 ___

The radius of the circle x2 + y2 + 2gx + 2fy + c = 0 is √g2 + f2 − c. The equation of the circle given x2 + y2 − 2x + 4y − 11 = 0 ⇒ g = −1 f=2 and c=11 ⇒ r = √(−1)2 + (2)2 − (−11) =√1+4+11 =√16 =4

Find the radius of the circle $x^{2} + y^{2} - 2 x + 4 y - 11 = 0$

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