Question

What type of conic section is represented by the parametric equations below? X=3cos(t)-1 y=3sin(t)+4

Answer 1

Circle

Explanation:

Examples of conic sections are the circle, the ellipse, the parabola and the hyperbola. Parametric equations are used to express the x and y variables in terms of a less complicated manner using a third variable (t or θ).

The parametric equation for a circle with an equation
`(x-h)^2+(y-k)^2=r^2` is given by:

`x=rcos(t)+h, y=rsin(t)+k`

where r is the radius of the circle and (h, k) is the center of the circle.

A conic section with a parametric equations X=3cos(t)-1, y=3sin(t)+4 is a circle with center at (-1, 4) and radius of 3. The equation of the circle is:

(x + 1)² + (y - 4)² = 3²