Step by step solution to "Eliminate the parameter and obtain the standard form..."

High School
Geometry
High school geometry
Conic sections

Suman Cole

Answered question

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. $(W h e n 0 \leq ? \leq 2 ? .)$ Circle: center: (6, 3), radius: 7

Answer & Explanation

stuth1

Skilled2020-12-28Added 97 answers

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

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

Squaring and adding $(x - h)^{2} + (y - k)^{2} = r^{2} \sin^{2} θ + r^{2} \cos^{2} θ$
$(x - h)^{2} + (y - k)^{2} = r^{2}$

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

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