# How do you graph #r=4/(-3+3sintheta)#?

##### 1 Answer

This is a hyperbola with its center

#### Explanation:

Multiply both sides by the denominator:

Multiply both side by -1:

Move the sine term to the right:

Factor out a 4:

Square both sides:

Substitute

Expand the square on the right:

distribute through the ()s:

Combine like terms and leave the constant on the right:

Add

Factor out -4 from the y terms

Use 8y to find the value of

This makes the left a perfect square with k:

Divide both sides by -48:

Put in standard form:

This is a hyperbola with its center