Question

The curve described parametrically by x=t2+t,y=2t−1 represents Parabola An ellipse Hyperbola Circle

Solution

The correct option is A Parabola x=t2+t and y=2t−1  By elimination of t  t=y+12 x=(y+12)2+y+12 y2+4y−4x+3=0  On comparing with ax2+by2+2hxy+2gx+2fy+c=0  we have a=0,b=1,g=−2,f=2,h=0,c=3 Δ=abc+2fgh−af2−bg2−ch2=−4≠0  and h2−ab=0⇒h2=ab So, the given equation is a parabola

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