Chapter H.1, Problem 22E

(a)

To determine

To decide: whether the given condition is easy to draw a polar equation or a Cartesian equation and write an equation for the curve.

Answer to Problem 22E

The curve would be more easily given by a Cartesian equation ${(x-2)}^2+{(y-3)}^2=5^2$

Explanation of Solution

Given:

A circle with radius 5 and center (2,3)

Calculation:

Since the center of the circle is not at the origin, so the curve would be more easily given by a Cartesian equation ${(x-2)}^2+{(y-3)}^2=5^2$

Conclusion:

Therefore, the curve would be more easily given by a Cartesian equation ${(x-2)}^2+{(y-3)}^2=5^2$ .

(b)

To determine

To decide: whether the given condition is easy to draw a polar equation or a Cartesian equation and write an equation for the curve.

Answer to Problem 22E

The curve would be more easily given by the polar equation

Cartesian equation is also simple as $x^2+y^2=4^2\Rightarrow x^2+y^2=16$

Explanation of Solution

Given:

A circle centered at the origin with radius 4.

Calculation:

Since the center of the circle is at the origin, so the curve would be more easily given by the polar equation as $[r=4]$ Cartesian equation is also simple as $x^2+y^2=4^2\Rightarrow x^2+y^2=16$

Conclusion:

Therefore, the curve would be more easily given by the polar equation.

Cartesian equation is also simple as $x^2+y^2=4^2\Rightarrow x^2+y^2=16$