Question

if (-1,4),(3,10) and (-1,2) are three points on a circle gind coordinates of centre​

Answer 1

Answer:

OA = OB = OC

Distance formula

(OA)2 = (OB)2

(h−1) 2+(k−2) 2 =h−3) 2 +(k+4) 2

h2 - 2h+1+k 2 −4k+4=h 2−6h+9+ k2 +8k+16

−2h−4k+5=−6h+8k+25

4h−12k=20⟹h−3k=5⟶(1)

OB 2 =OC 2(h−3) 2 +(k+4) 2 =(h−5) 2+(k+6) 2h 2 −6h+9+k 2 +8k+16=h 2

−10h+25+k 2

+12k+36

−6h+8k+25=−10h+12k+61

⟹4h−4k=36⟹h−k=9⟶(2)

−2k=−4

h−3k=5−h±k=−9

∴k=2∴h=11

∴ The Coordinates are (h,k)=(11,2)

Answer 2

Answer:

given,

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