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Question

For the curve which is described parametrically by x=t2+t and y=t2t, the value of |Δ| is

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Solution

Parametric equations are
x=t2+t (1)y=t2t (2)
From (1)+(2), we get
x+y2=t2 (3)
From (1)(2), we get
xy2=t (4)

Now from (3) and (4), we have
x+y2=(xy2)2x2+y22xy2x2y=0
Comparing the above equation with general form of conic equation, we get
a=b=1,h=1,g=f=1,c=0
Δ=02110=4|Δ|=4

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