Find the centre of a circle passing through the points (6,−6),(3,−7) and (3,3).

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Filo · Accepted Answer

Let O(x,y) is the center of the circle and A(6.−6),B(3,−7) and C(3,3)are the points on the circumference of the circle.∴OA=(x1​−x2​)2+(y1​−y2​)2​⇒OA=(x−6)2+(y+6)2​⇒OB=(x−3)2+(y+7)2​⇒OC=(x−3)3+(y−3)2​∵ Radii of the circle are equal ∴OA=OB⇒(x−6)2+(y+6)2​=(x−3)2+(y+7)2​⇒x2+36−12x+y2+36+12y=x2+9−6x+y2+49+14y⇒−6x−2y+14=0⇒3x+y=7....................................................................(i)Similarly, OA=OC⇒(x−6)2+(y+6)2​=(x−3)2+(y−3)2​⇒x2+36−y+y2+36+12y=x2+9−6x+y2+9−6y⇒−6x+18y+54=0⇒−3x+9y=−27............................................................(ii)Adding (i) and (ii)⇒10y=−20⇒y=−2Substitute the value of y in  (i)⇒3x+−2=7⇒3x=9⇒x=3∴ The center of the circle is (3,−2).

Question Text	Find the centre of a circle passing through the points $(6, - 6), (3, - 7)$ and $(3, 3)$ .
Answer Type	Text solution:1
Upvotes	150

Find the centre of a circle passing through the points $(6, - 6), (3, - 7)$ and $(3, 3)$ .

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