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The equation r=3cosθ represents a circle. Find the cartesian coordinates of the center, x=?,y=?, and radius=?

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The equation r=3cosθ represents a circle. Find the cartesian coordinates of the center, x=?,y=?, and radius=?

asked Feb 7, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The equation is image.

The polar coordinates are related to cartesian coordinates by the equation .

Where .

Change the polar equation into cartesian equation.

image

Multiply each side by .

image

Substitute and .

image

image

Step 2:

Convert the equation image in standard form.

Change the expression image into a perfect square trinomial,

add (half the x coefficient)² to each side of the equation.

image

image

Compare above equation with circle standard equation .

Where is center of circle and is the radius of circle.

The equation image is in the form of circle equation image.

center of circle is image.

Radius of circle is image.

Solution:

The circle equation is image.

Center of circle is image.

Radius of circle is image.

answered Feb 8, 2015 by Sammi Mentor

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