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$x=a \cos(t), y=b \sin(t)$ is the parametric form of

  1. Ellipse
  2. Hyperbola
  3. Circle
  4. Parabola
in Calculus by Veteran (106k points) | 1.2k views
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Parametric equations:

hyperbola: x= a sec t, y=b tan t

parabola: x= at^2, y= 2at

1 Answer

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Answer A) Ellipse

x=a cos t

or, x2=a2cos2t

or, $\frac{x^2}{a^2}$ =cos2t.......................i

y=b sin t

or,y2=b2sin2t

or,$\frac{y^2}{b^2}$ = sin2t........................ii

from i and ii

 $\frac{x^2}{a^2}$ +$\frac{y^2}{b^2}$ =cos2t+sin2t =1

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