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Question
Eliminate θ from the following :
x = 6cosecθ, y = 8cotθ
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Solution
x = 6cosecθ and y = 8cotθ
∴ cosecθ = `x/6 and cot theta = y/8`
We know that,
∴ cosec2θ – cot2θ = 1
`(x/6)^2 - (y/8)^2` = 1
∴ `x^2/36 - y^2/64` = 1
∴ `(64x^2 - 36y^2)/(36 xx 64)` = 1
∴ `(64x^2 - 36y^2)/2304` = 1
∴ 64x2 – 36y2 = 2304
Divided by 4
∴ 16x2 – 9y2 = 576
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