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

Let P be the point ((a/2)(t^2 +(1/t^2 )),a(t−(1/t)))  Find the locus of P, as t varies.

LetPbethepoint(a2(t2+1t2),a(t1t))FindthelocusofP,astvaries.

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

Let P be the point ((a/2)(t^2 +(1/t^2 )),a(t−(1/t)))  Find the locus of P, as t varies.  Put x=(a/2)((1/t^2 )+t^2 ),y=a(t−(1/t))  ⇒((y/a))^2 =t^2 +(1/t^2 )−2=((2x)/a)−2  ⇒y^2 =2ax−2a^2 ⇒P is on the Parabol  y^2 =2ax−2a^2

LetPbethepoint(a2(t2+1t2),a(t1t))FindthelocusofP,astvaries.Putx=a2(1t2+t2),y=a(t1t)(ya)2=t2+1t22=2xa2y2=2ax2a2PisontheParaboly2=2ax2a2

Commented by ZiYangLee last updated on 19/May/21

thank you sir

thankyousir

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