1. ## Name the Curve

Name the curve with the given polar equation

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

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

Circle with radius 4 and origin (0,0)

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

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

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

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

$=> r^2=-4x$

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

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

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) $r=4$
$r^2=4^2

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

Circle with radius 4 and origin (0,0)

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

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

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

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

$=> r^2=-4x$

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

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

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.