a.
(xβ3)2+(y+1)2=5 The coordinates of the centre of the circle are D(3,β1).
If AB is the diameter of the circle, then D is the midpoint of AB
xDβ=2xAβ+xBββ=>xBβ=2xDββxAβ
yDβ=2yAβ+yBββ=>yBβ=2yDββyAβ
xBβ=2(3)β1=5,yBβ=2(β1)β(β2)=0 Point B(5,0)
b.
Point C(2,1)
CA=β¨1β2,β2β1β©
CB=β¨5β2,0β1β©
CAβ
CB=β1(3)+(β3)(β1)=β3+3=0
β£CAβ£ξ =0,β£CBβ£ξ =0 Therefore CAβ₯CB, and β ACB=90Β°.
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