The radius of the circle x2-y2-2 x-4 y-11-0is-A- -1 unitsB- 2 unitsC- 11 unitsD- 4 units

The correct option is D 4 unitsThe radius of a nbsp;circle x^2 + y^2 + 2gx + 2fy + c = 0 is √(g^2 + f^2 c). Given, the equation is x^2 + y^2 2x + 4y 11 ...

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Standard X

Mathematics

Equation of the Circle Using End Points of Diameter

The radius of...

Question

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

-1 units

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2 units

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11 units

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4 units

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Solution

The correct option is D 4 units
The radius of a circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$
is $\sqrt{g^{2} + f^{2} - c}$ .

Given, the equation is
$x^{2} + y^{2} - 2 x + 4 y - 11 = 0$

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

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

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

$= \sqrt{16} = 4 u n i t s$

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The radius of the circle x2 + y2 − 2x + 4y − 11 = 0 is .

The correct option is D 4 unitsThe radius of a circle x2 + y2 + 2gx + 2fy + c = 0 is √g2 + f2 − c. Given, the equation is x2 + y2 − 2x + 4y − 11 = 0 ⇒ g = −1, f=2 and c=−11 ⇒ r = √(−1)2 + (2)2 − (−11) =√1+4+11 =√16=4 units

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