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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. |
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Answer» 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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