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Question

The Locus of the point (tanθ+sinθ,tanθsinθ) is (xmym)m=axy. Find a×m

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Solution

locus of the point (tanθ+sinθ,tanθsinθ)
x=tanθ+sinθ
y=tanθsinθ
tanθ=x+y2,sinθ=xy2
cosθ=xyx+y
sin2θ+cos2θ=1
(xy)24+(xy)2(x+y)2=1
(xy)2[4+(x+y)2]=4(x+y)2
(x+y)2(xy)2=4[(x+y)2(xy)2]
(x+y)2=4[4xy]
(x2y2)2=16xy
a=16,m=2
axm=16×2=32

1115544_1035822_ans_77fa04c9a5044e56924137369f0f0c68.jpg

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