Let-P-be-the-point-a-2-t-2-1-t-2-a-t-1-t-Find-the-locus-of-P-as-t-varies-

Question Number 141446 by ZiYangLee last updated on 19/May/21

Let P be the point (\frac{a}{2} (t^{2} + \frac{1}{t^{2}}), a (t - \frac{1}{t}))

Find the locus of P, as t varies .

Answered by 1549442205PVT last updated on 19/May/21

Let P be the point (\frac{a}{2} (t^{2} + \frac{1}{t^{2}}), a (t - \frac{1}{t}))

Find the locus of P, as t varies .

Put x = \frac{a}{2} (\frac{1}{t^{2}} + t^{2}), y = a (t - \frac{1}{t})

\Rightarrow {(\frac{y}{a})}^{2} = t^{2} + \frac{1}{t^{2}} - 2 = \frac{2 x}{a} - 2

\Rightarrow y^{2} = 2 ax - {2 a}^{2} \Rightarrow P is on the Parabol

y^{2} = 2 ax - {2 a}^{2}

Commented by ZiYangLee last updated on 19/May/21

thank you sir