x = a cos(t), y = b sin(t) is the parametric form of
2009
x = a cos(t), y = b sin(t) is the parametric form of
- A.
Ellipse
- B.
Hyperbola
- C.
Circle
- D.
Parabola
Show answer & explanation
Correct answer: A
The parametric equations x = a cos(t) and y = b sin(t) describe an ellipse. By squaring both equations and dividing by the constants, we get (x/a)^2 = cos^2(t) and (y/b)^2 = sin^2(t). Adding these yields x^2/a^2 + y^2/b^2 = cos^2(t) + sin^2(t) = 1, which is the standard Cartesian equation of an ellipse.