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Question
Eliminate θ from the following:
x = 3secθ , y = 4tanθ
Solution
x = 3sec θ and y = 4tan θ
∴ sec θ = `x/3 and tan theta = y/4`
We know that,
sec2θ – tan2θ = 1
∴ `(x/3)^2 - (y/4)^2` = 1
∴ `x^2/9 - y^2/16` = 1
∴ `(16x^2 - 9y^2)/(16 xx 9)` = 1
∴ `(16x^2 - 9y^2)/144` = 1
∴ 16x2 − 9y2 = 1 x 144
∴ 16x2 – 9y2 = 144
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