The curve described parametrically by x = t² + t + 1 and y = t² - t + 1 is

A)St line

B)Ellipse

C)Parabola

D)Hyperbola

Dear Pritish,

The parametric equations given are

X = t² + t + 1 and y = t² – t +1

Or,  x = t² + t + 1        (i)

        y = t² – t +1         (ii)

  -          -      +   -

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x – y = 2t

This is the equation of a straight line. You change the parameter t, you get different lines.

Um, actually, on solving you get,

x + y = 2(t^2 + 1)

x - y = 2t

and hence, x^2 + y^2 - 2xy - 2x - 2y + 4 = 0

which turns out to be a parabola, right?

yes it will be a parabola. not a straight line.