The circumcenter of the equilateral triangle having the three points \theta_1, \theta_2, \theta_3 lying on the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 as its vertices is (r, s). Then the average of \cos (\theta_1-\theta_2), \cos (\theta_2-\theta_3) and \cos (\theta_3-\theta_1) is

Correct Answer is : 12[3r2a2+3s2b2−1]

\frac{1}{2} [\frac{3 r^2}{a^2}+\frac{3 s^2}{b^2}-1]

\frac{3}{2} [\frac{r^2}{a^2}+\frac{s^2}{b^2}]

\frac{1}{3} [\frac{r^2}{a^2}+\frac{s^2}{b^2}]

\frac{1}{3} [\frac{r^2}{a^2}+\frac{s^2}{b^2}+\frac{r s}{a b}]

TG EAMCET 4 May 2025 Shift 2 Paper

Question : 55 of 160

Marks: +1, -0

The circumcenter of the equilateral triangle having the three points θ1,θ2,θ3 lying on the ellipse ‌

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=1 as its vertices is (r,s). Then the average of cos(θ1−θ2), cos(θ2−θ3) and cos(θ3−θ1) is

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