The equations x - t-4 - y - t2-4 represents

Eliminating t, we get 16x^2=4y ⇒ x^2=1/4 y, which is a parabola. ...

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Four Common Forms of Parabola Equation

The equations...

Question

The equations $x = \frac{t}{4}, y = \frac{t^{2}}{4}$ represents

A circle

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A parabola

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An ellipse

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A hyperbola

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Solution

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x = \frac{t}{4}, y = \frac{t^{2}}{4}

x = a (\frac{1 - t^{2}}{1 + t^{2}}), y = \frac{2 b t}{1 + t^{2}}; t \in R

x = t^{2} + t + 1

y = t^{2} - t + 1

x = \frac{t}{4}, y = \frac{t^{2}}{4}

x = t^{2} + t + 1, y = t^{2} - t + 1

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