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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)
- - + -
---------------------
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.
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