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
ANSWERED
asked 2020-12-27

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

Expert Answers (1)

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 \(x = 6 + 7 \cos \theta\)
\(7 = 3 + 7 \sin \theta\)

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