Find the locus of the point (t^2+t+1,t^2...

Find the locus of the point `(t^2+t+1,t^2-t+1),t in Rdot`

Text Solution

Verified by Experts

Let `(h,h)-=(t^2-t+1,t^2+t+1)`
or `h=t^2-t+1` and `k=t^2+t+1`
or `k-h=2t`
or `t=(k-h)/(2)`
or `h=((k-h)/(2))^(2)-((k-h)/(2))+1`
The required locus is
`x=((x-y)/(2))^2-((y-x)/(2))+1`

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