Mathematics · Coordinate Geometry
The circumcenter of an equilateral triangle with vertices at points having eccentric angles θ1, θ2, and θ3 on the ellipse x2a2 + y2b2 = 1 is (r, s). Then, the average of cos(θ1 - θ2), cos(θ2 - θ3), and cos(θ3 - θ1) is equal to:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 132 [ r2a2 + s2b2 ]
- 213 [ r2a2 + s2b2 + rsab ]
- 313 [ r2a2 + s2b2 ]
- 412 [ 3r2a2 + 3s2b2 - 1 ]✓
Correct answer
12 [ 3r2a2 + 3s2b2 - 1 ]
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