Answer:
Step-by-step explanation:
The general equation for any conic section is:
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0,
where A, B, C, D, E, F are fixed coefficients and A, B, C are not simultaneously equal to 0.
But, we can also write equations for conic section in terms of trigonometric functions using Parametric Equations:
For circle:
(x, y) = (rcos(theta), rsin(theta)) <=> x^2 + y^2 = r^2,
because (cos(theta))^2 + (sin(theta))^2 = 1
For ellipse:
(x, y) = (acos(theta), bsin(theta)) or x^2/a^2 + y^2/b^2 = 1
because (cos(theta))^2 + (sin(theta))^2 = 1
For hyperbola:
(x, y) = (asec(theta), btan(theta)) or x^2/a^2 - y^2/b^2= 1
because (cos(theta))^2 + (sin(theta))^2 = 1
