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The curve described parametrically by x = t 2 + t + 1 and y = t 2 - t + 1 is A)St line B)Ellipse C)Parabola D)Hyperbola

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


A)St line


B)Ellipse


C)Parabola


D)Hyperbola

Grade:12

3 Answers

Askiitians Academic Expert
8 Points
12 years ago

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)

  -          -      +   -

---------------------

x – y = 2t

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

Mardava Rjgpl
18 Points
11 years ago

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?

saumya singla
18 Points
8 years ago

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

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