Question

For $t \in(0,2 \pi)$, if $ABC$ is an equilateral triangle with vertices$A ( \sin t, -{\cos t}), B ( \cos t, \sin t )$ and $C ( a , b )$ such that its orthocentre lies on a circle with centre $\left(1, \frac{1}{3}\right)$, then $\left(a^2-b^2\right)$ is equal to :

• A. $\frac{8}{3}$
• B. 8
• C. $\frac{77}{9}$
• D. $\frac{80}{9}$

Answer 1

Answer: (B)

8

Answer 2

From the given options the correct answer is option (B): 8