jee-main 2022 Q65

jee-main · India · session2_28jul_shift1 Straight Lines & Coordinate Geometry Triangle Properties and Special Points

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 $a^2 - b^2$ is equal to
(1) $\frac{8}{3}$
(2) $8$
(3) $\frac{77}{9}$
(4) $\frac{80}{9}$

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 $a^2 - b^2$ is equal to\\
(1) $\frac{8}{3}$\\
(2) $8$\\
(3) $\frac{77}{9}$\\
(4) $\frac{80}{9}$

Paper Questions

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