Question

In the figure, if AOBA is an equilateral, then find
co-ordinates of vertex B.
​

Answer 1

Answer:

( a, a√3 )

Step-by-step explanation:

B(x, y) and (x, y) ∈ I quadrant ⇒ x > 0 , y > 0 and a > 0

OA = OB = AB = 2a

(x - 0)² + (y - 0)² = 4a² ⇒ x² + y² = 4a² .......... (1)

(x - 2a)² + (y - 0)² = 4a² ⇒ (x - 2a)² + y² = 4a² ....... (2)

(2) - (1) :

(x - 2a)² - x² = 0

x² - 4ax + 4a² - x² = 0 ⇒ x = a

x = a ----> (1)

a² + y² = 4a² ⇒ y = a√3

( a, a√3 )