1. ## Name the Curve

Name the curve with the given polar equation

1) $\displaystyle r=4$
$\displaystyle r^2=4^2$

$\displaystyle x^2+y^2=4^2$

Circle with radius 4 and origin (0,0)

2)$\displaystyle \Theta=\dfrac{2\Pi}{3}$
Stumped.

3)$\displaystyle r=-4\cos\Theta$

$\displaystyle \cos\Theta=\dfrac{x}{r}$

$\displaystyle => r=-4\dfrac{x}{r}$

$\displaystyle => r^2=-4x$

$\displaystyle x^2+4x+y^2=0$

$\displaystyle (x+2)^2+y^2=2^2$

Circle with radius 2 and origin (-2,0)

If someone could verify 1 & 3 and help with the 2 I would be most appreciative. Thanks.

2. Originally Posted by Len
Name the curve with the given polar equation

1) $\displaystyle r=4$
$\displaystyle r^2=4^2 x^2+y^2=4^2$

Circle with radius 4 and origin (0,0)

2)$\displaystyle \Theta=\dfrac{2\Pi}{3}$
Stumped.

3)$\displaystyle r=-4\cos\Theta$

$\displaystyle \cos\Theta=\dfrac{x}{r}$

$\displaystyle => r=-4\dfrac{x}{r}$

$\displaystyle => r^2=-4x$

$\displaystyle x^2+4x+y^2=0$

$\displaystyle (x+2)^2+y^2=2^2$

Circle with radius 2 and origin (-2,0)

If someone could verify 1 & 3 and help with the 2 I would be most appreciative. Thanks.
1) Correct
2) Only an angle is specified. Hence r can be anything. Hence it is just an infinite straight line at that angle from the positive x axis.
3) Correct.