99 Percentile Qs Bank for JEE MainMathematicsEllipse

If B is end point of minor axis of the ellipse b² x²+a² y²=a² b²(a>b) and S and S' are foci of ellipse such that SBS ^ is an equilateral triangle, then eccentricity e =

Options

A1 2
B1 3
C3 5
D4 5

Correct answer

A. 1 2

Step-by-step solution

Correct option is A Given S (- ae , 0), T ( ae , 0), B (0, ~b ) As STB is an equilateral triangle In TOB 60^ = OB OS 3 = OB OS = b ae ( 3 a e)²=b²3 a² (1- b² a² )=b²3 (1- b² a² )= b² a² 3 4 = b² a² e= 1- 3 4 = 1 2

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