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Question

The conic section represented by the equations x = t2+t+1 and y = t2t+1 is ________ .

A
hyperbola
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B
point
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C
parabola
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D
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Solution

The correct option is C parabola
Given equations are x = t2+t+1 and y = t2t+1.
x+y = 2t2+2 and xy=2t
x+y = 2t2+2 2(x+y)=(2t)2+42(x+y)=(xy)2+4x2+y22xy2x2y+4=0
Here, a = 1, b = 1, h = -1, g = -1, f = -1, c = 4.
Now, = abc + 2fgh af2bg2ch2 = 40And h2=ab
So, the given equation represents a parabola.

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