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Question

The radius of the circle S is same as the radius of x2 + y2 âˆ’ 2x + 4y âˆ’ 11 = 0 and the centre of S is the centre of x2 + y2 âˆ’ 2x âˆ’ 4y + 11 = 0 . Find the equation of S.

A

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B

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C

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D

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Solution

The correct option is C To find the equation of a circle, we need the centre and radius of the circle, In this problem, we are given two circles, using which we can find the centre and radius. To find the radius x2 + y2 − 2x + 4y − 11 = 0 and S(our circle) has the same radius. We know the radius of the circle x2 + y2 + 2gx + 2fy + c=0 is √g2 + f2 − c ⇒ r = √12 + 22 + 11 =4 To find the centre: We are given S and x2 + y2 − 2x − 4y + 11 = 0 have the same centre Centre of x2 + y2 + 2gx + 2fy + c=0 is (−g,−f). ⇒ centre of x2 + y2 − 2x − 4y + 11 = 0 is (1,2) We got the centre (1,2) and radius (4) of the circle. ⇒ Equation is (x−1)2 + (y−2)2 = 42 ⇒ x2 + y2 − 2x − 4y + 1 + 4 = 16 ⇒ x2 + y2 − 2x − 4y − 11 = 0

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