Eliminate 0 from the following: x = 3sec θ, y = 4tan θ

1.	Eliminate 0 from the following: x = 3sec θ, y = 4tan θ
Answer» x = 3sec θ, y = 4tan θ ∴ sec² θ = x/3 and tan θ = y/4 We know that, sec²θ - tan²θ = 1 ∴ \((\frac{x}{3})^2 - (\frac{y}{4})^2 = 1\) ∴ \(\frac {x^2}{9} - \frac{y^2}{16}=1\) ∴ 16x² – 9y² = 144

Answer»

x = 3sec θ, y = 4tan θ

∴ sec² θ = x/3 and tan θ = y/4

We know that,

sec²θ - tan²θ = 1

∴ \((\frac{x}{3})^2 - (\frac{y}{4})^2 = 1\)

∴ \(\frac {x^2}{9} - \frac{y^2}{16}=1\)

∴ 16x² – 9y² = 144

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