Convert the polar equation r = 4*cos(theta) into Cartesian (rectangular) coordinates.
Answer and explanation
Correct answer: A. (x - 2)^2 + y^2 = 4
- Step 1: Multiply both sides by r: r^2 = 4rcos(theta).
- Step 2: Substitute r^2 = x^2 + y^2 and r*cos(theta) = x: x^2 + y^2 = 4x. Complete the square: (x - 2)^2 + y^2 = 4.
Answer
(x - 2)^2 + y^2 = 4.
Why not the others: 'x^2 + (y - 2)^2 = 4' assumes rsin(theta) = y instead of rcos(theta); 'x^2 + y^2 = 16' forgets the directional dependence on cos(theta); '(x - 4)^2 + y^2 = 16' does not divide 4 by 2 when completing the square.
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