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Show that the curve whose parametric coordinates are `x=t^(2)+t+l,y=t^(2)-t+1` represents a parabola.

Text Solution

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From the given relations, we have `(x+y)/(2)=t^(2)+1,(x-y)/(2)=t`
Eliminating t, we get
`2(x+y)=(x-y)^(2)+4`
This is second-degree equation in which second-degree terms form perfect square.
Rewriting the equation, we have
`x^(2)+y^(2)-2xy-2x-2y+4=0`
Comparing with `ax^(2)+by^(2)+2hxy+2gx+2fy+c=0`, we find that `abc+2fgh-af^(2)-bg^(2)-ch^(2)!=0`.
So, given equation represents a parabola.
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