Question

For each of the described curves, decide if the curve would be more easily given by a polar equation or a Cartesian equation. Then write an equation for the curve. (a) A circle with radius 2 and center (3, 2).
(b) A circle centered at the origin with radius 1.

Answer 1

The equation of circle for both the parts will be as,

(a)  (x-3)² +(y-2)²= 4

(b)   x²+y² = 1

What is circle?

A circle may be a form consisting of all purposes in a very plane that ar at a given distance from a given point, the centre. Equivalently, it's the curve copied out by a point that moves in a very plane so its distance from a given point is constant.

Main Body:

(a) When the circle is offset from the origin, the equation for the radius gets messy. In general, it will be the root of a quadratic equation in sine and cosine, not easily simplified. The Cartesian equation is easier to write.

Circle centered at (h, k) with radius r:

(x -h)² +(y -k)² = r²

The given circle is ...

(x -2)² +(y -2)² =2²

(x -2)² +(y -2)² = 4

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(b) When the circle is centered at the origin, the radius is a constant. The desired circle is most easily written in polar coordinates:

x²+y² = 1

Hence the equation of circle is such.

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