Question

(-2,2),(x,8),( 6,y) are three concyclic points whose centre is (2,5). find the possible value of x and y​

Answer 1

Let the given points beA(−2,2),B(x,8),C(6,y) and O(2,5).

Here, OA=OB=OC⇒OA2=OB2=OC2 .......... (Radii of same circle)

Now, OA2=(−2−2)2+(2−5)2=(−4)2+(−3)2=16+9=25

OB2=(X−2)2+(8−5)2=(X−2)2+9

OC2=(6−2)2+(Y−5)2=42+(Y−5)2=16+(Y−5)2

Since, OA2=OB2=OC2, we have

(x−2)2+9=25  and 16+(y−5)2=25

⇒(x−2)2=16 and (y-5)^2 = 9

⇒x−2=±4  and y−5=±3

⇒x=6,−2 and y=8,2

Hence, x=6,−2 and y=8,2

Answer 2

Answer:

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