If θ is the angle between the lines joining the origin to the points of intersection of the curve 2 x 2 + 3 y 2 = 6 and the line x + y = 1 , then sin θ =

Question

If θ is the angle between the lines joining the origin to the points of intersection of the curve 2 x 2 + 3 y 2 = 6 and the line x + y = 1 , then sin θ =, 1, 7 145, 96 145, 1 2

MARKS App · Accepted Answer

The homogenised equation of 2 x 2 + 3 y 2 = 6 and x + y = 1 is 2 x 2 + 3 y 2 - 6 ( x + y ) 2 = 0 ⇒ - 4 x 2 - 3 y 2 - 12 x y = 0 ⇒ 4 x 2 + 3 y 2 + 12 x y = 0 tan θ = 2 6 2 - 12 7 = 4 6 7 sin θ = 4 6 145 = 96 145

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