A circle is concentric with circle $x^{2} + y^{2} - 2 x + 4 y - 20 = 0$ . If perimeter of the semicircle is $36$ then the equation of the circle is :

x^{2} + y^{2} - 2 x - 4 y - 44 = 0

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(x - 1)^{2} + (y + 2)^{2} = (126 / 11)^{2}

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x^{2} + y^{2} - 2 x + 4 y - 43 = 0

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Solution

The correct option is B $(x - 1)^{2} + (y + 2)^{2} = (126 / 11)^{2}$
$x^{2} + y^{2} - 2 x + 4 y - 20 = 0$
center $(1, - 2)$
perimeter $\Rightarrow 36 = (π r + 2 r)$
$36 = r (3.14 + 2) =$
$((x - 1) + y + 2)^{2} = {(\frac{126}{11})}^{2}$ or $(7)^{2}$ $r = \frac{36}{5.14} = 7$

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A circle is concentric with circle x2+y2−2x+4y−20=0. If perimeter of the semicircle is 36 then the equation of the circle is :

The correct option is B (x−1)2+(y+2)2=(126/11)2x2+y2−2x+4y−20=0center (1,−2)perimeter ⇒36=(πr+2r) 36=r(3.14+2)=((x−1)+y+2)2=(12611)2 or (7)2 r=365.14=7

A circle is concentric with circle $x^{2} + y^{2} - 2 x + 4 y - 20 = 0$ . If perimeter of the semicircle is $36$ then the equation of the circle is :

The correct option is B $(x - 1)^{2} + (y + 2)^{2} = (126 / 11)^{2}$
$x^{2} + y^{2} - 2 x + 4 y - 20 = 0$
center $(1, - 2)$
perimeter $\Rightarrow 36 = (π r + 2 r)$
$36 = r (3.14 + 2) =$
$((x - 1) + y + 2)^{2} = {(\frac{126}{11})}^{2}$ or $(7)^{2}$ $r = \frac{36}{5.14} = 7$