Question

# Eliminate the parameter and obtain the standard form of the rectangular equation.Circle: x = h + r cos(?), y = k + r sin(?)Use your result to find a set of parametric equations for the line or conic section. (When 0 leq ? leq 2?.)Circle: center: (6, 3), radius: 7

Conic sections

Eliminate the parameter and obtain the standard form of the rectangular equation. Circle: $$x = h + r \cos(?), y = k + r \sin(?)$$ Use your result to find a set of parametric equations for the line or conic section. $$(When\ 0 \leq ? \leq 2?.)$$ Circle: center: (6, 3), radius: 7

2020-12-28

Step 1: Given $$x = h + r \cos \theta , y = k + \sin \theta$$

Step 2: Solution $$x = h + r \cos \theta , y = k + \sin \theta$$
$$x − h = r \cos \theta, y − k = r \sin \theta$$

Squaring and adding $$(x − h)^2 + (y−k)^2 = r^2 \sin^2 \theta + r^2 \cos^2 \theta$$
$$(x − h)^2 + (y−k)^2 = r^2$$

With (6,3), radius = 7 $$x = 6 + 7 \cos \theta$$
$$7 = 3 + 7 \sin \theta$$