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Asymptotes

Find the locu...

Question

Find the locus of the point(t²-t+1,t²+t+1), t belongs to R.

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Solution

Put X=t^2+t+1
y=t^2-t+1
Solve this equations to eliminate the t.

x+y=2(t^2+1)
Let x-y=2t
x+y=(1/2)(x-y)^2+2
On rearranging
X^2-2xy+y^2-2x-2y+4=0
Then compare with the general equation of second degree equation i.e. ax²+by²+2hxy+2gx+2fy+c=0. Then you will find that Since, abc+2fgh-af²-bg²-ch² is not equal to zero and h²=ab. Therefore this equation will represent a parabola

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