Eliminate the parameter \theta in the following parametric equations x=a\tan\theta\ y=b\sec\theta

europaparksn

europaparksn

Answered question

2021-11-29

Eliminate the parameter θ in the following parametric equations
x=atanθ y=bsecθ

Answer & Explanation

Michele Grimsley

Michele Grimsley

Beginner2021-11-30Added 19 answers

Step 1
we have to eliminate the parameter θ in the following parametric equations:
x=atanθ
y=bsecθ
as x=atanθ
Therefore,
1) tanθ=xa
as y=bsecθ
therefore,
2) secθ=yb
Step 2
as we know that:
sec2θtan2θ=1
therefore,
(secθ)2(tanθ)2=1
(yb)2(xa)2=1 (from equation (1) and (2))
y2b2x2a2=1
therefore the equation of the hyperbola obtained after eliminating the parameter θ in the parametric equations is:
y2b2x2a2=1

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