UPSEE 2017 Solved Paper

Given, OAB is an equilateral triangle.

Let C is the middle point of side AB
∴ Coordinate of C ≡(

a+b

2

,

11+37

2

)
≡(

a+b

2

,24)
∵OAB is an equilateral triangle.
∴OC=√3CA
⇒(OC)2=(√3CA)2 [By squaring both side]
⇒(OC)2=3(CA)2
⇒(

a+b

2

−0)2+(24−0)2=3 [(a−

a+b

2

)2+(11−24)2]
⇒

a2+b2+2ab

4

+576 =3[(

a−b

2

)2+(−13)2]
⇒

a2+b2+2ab+2304

4

=3 [

a2+b2−2ab+169×4)

4

]
⇒a2+b2−4ab=138