### All Precalculus Resources

## Example Questions

### Example Question #21 : Convert Polar Equations To Rectangular Form

Write the equation for in rectangular form

**Possible Answers:**

**Correct answer:**

First multiply both sides by cosine

Now we can make the substitutions and

add 2 to both sides

square both sides

multiply both sides by the denominator

distribute on the left side

subtract from both sides

factor out y squared

divide both sides by

take the square root

### Example Question #21 : Convert Polar Equations To Rectangular Form

Which is equivalent to in rectangular form?

**Possible Answers:**

**Correct answer:**

Multiply both sides by r squared

Now we can substitute and

square both sides

### Example Question #23 : Convert Polar Equations To Rectangular Form

Which is equivalent to in rectangular form?

**Possible Answers:**

**Correct answer:**

First multiply both sides by r:

Now make the substitutions and :

add to both sides

subtract x squared and y squared from both sides

square both sides

### Example Question #24 : Convert Polar Equations To Rectangular Form

Write in rectangular form

**Possible Answers:**

**Correct answer:**

multiply both sides by r:

Now we can make the substitutions , , and :

If we subtract the terms on the right from both sides, we can complete the square twice and make this into a regular circle equation:

To complete the square for x, add 1, since .

To complete the square for y, add since .

re-write the left side as binomials squared:

### Example Question #25 : Convert Polar Equations To Rectangular Form

Write the equation for in rectangular form.

**Possible Answers:**

**Correct answer:**

Multiply both sides by r:

Now we can substitute in , , and .

if we subtract both terms on the right from both sides, we can complete the square twice to get this into the normal form for a circle.

To complete the square for x, add 1 to both sides, since

To complete the square for y, add 16 to both sides, since :

Re-write the left side as two binomials squared

### Example Question #26 : Convert Polar Equations To Rectangular Form

Write the equation for in rectangular form

**Possible Answers:**

**Correct answer:**

To convert, make the substitutions and :

square both sides

multiply both sides by

subtract from both sides

subtract from both sides

factor our

divide both sides by

take the square root of both sides

### Example Question #27 : Convert Polar Equations To Rectangular Form

Convert the equation to rectangular form

**Possible Answers:**

**Correct answer:**

Multiply both sides by :

distribute

multiply both sides by r

convert to rectangular by making the substitutions , , and :

subtract 8x from both sides and combine like terms

complete the square for x by adding 16 to both sides

divide both sides by 16