The correct option is A 4
Let the given points be A(0,0),B(a,2),C(2,b)
Since, A,B,C are the vertices of equilateral triangle,
⇒AB=BC=AC
By using distance formula, we have
AB=√a2+4 ⋯(1)
Similarly, BC=√(a−2)2+(b−2)2 ⋯(2)
and AC=√4+b2 ⋯(3)
Equating equation (1) and (3), we get
√4+a2=√4+b2
⇒a2+4=b2+4
⇒a=±b
Since a and b lie in (0,2),
⇒ Both a and b are positive.
∴a=b
Now, 4(a+b)−ab=8a−a2
Equating equation (1) and (2), we get
√(a−2)2+(b−2)2=√a2+4⇒a2−8a+4=0
Hence, 4(a+b)−ab=8a−a2=4