The curve described parametrically by x - t 2- t -1- y - t 2- t -1 representsA- a pair of straight linesB- an ellipseC- a hyperbolaD- a parabola

The correct option is D a parabola x + y/2 = t^2 + 1, x y/2 = t Eliminating, t, 2(x + y) = (x y)^2 + 4 Since 2nd degree terms form a perfect square, it rep ...

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Standard XII

Mathematics

Parametric Equation of Parabola

The curve des...

Question

The curve described parametrically by $x = t^{2} + t + 1, y = t^{2} - t + 1$ represents

a pair of straight lines

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an ellipse

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a parabola

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a hyperbola

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Solution

The correct option is C a parabola
$\frac{x + y}{2} = t^{2} + 1, \frac{x - y}{2} = t$
Eliminating, t, $2 (x + y) = (x - y)^{2} + 4$
Since 2nd degree terms form a perfect square, it represents a parabola.

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The curve described parametrically by x=t2+t+1,y=t2−t+1 represents

The correct option is C a parabola x+y2=t2+1,x−y2=t Eliminating, t, 2(x+y)=(x−y)2+4 Since 2nd degree terms form a perfect square, it represents a parabola.

The curve described parametrically by $x = t^{2} + t + 1, y = t^{2} - t + 1$ represents

The correct option is C a parabola
$\frac{x + y}{2} = t^{2} + 1, \frac{x - y}{2} = t$
Eliminating, t, $2 (x + y) = (x - y)^{2} + 4$
Since 2nd degree terms form a perfect square, it represents a parabola.