Question

If teta is a parameter, find the equation of the locus of a moving point whose coordinates are (a sec. theta b tan theta)

Answer 1

SOLUTION

TO DETERMINE

θ is a parameter, find the equation of the locus of a moving point whose coordinates are (a sec θ , b tan θ )

EVALUATION

Here it is given that θ is a parameter

We have to find the locus of a moving point whose coordinates are (a sec θ , b tan θ )

Let h = a sec θ , k = b tan θ

Then

$\displaystyle \sf{ \frac{h}{a} = \sec \theta \: \: and \: \: \frac{k}{b} = \tan \theta}$

We know that

$\displaystyle \sf{ {\sec}^{2} \theta - { \tan }^{2} \theta = 1}$

$\displaystyle \sf{ \implies \: \frac{ {h}^{2} }{ {a}^{2} } - \frac{ {k}^{2} }{ {b}^{2} } = 1 }$

So the required locus is

$\displaystyle \sf{ \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1 }$

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