In this worksheet, we will practice extracting the radius and center of a circle from its equation.

**Q3: **

A circle is the translation of circle by . What is its equation?

- A
- B
- C
- D

**Q4: **

Given that the equation of the given circle is , find the length of .

**Q5: **

What are the relative positions of circles and ?

- AThe two circles touch externally.
- BThe two circles are disjoint.
- CThe two circles touch internally.
- DThe two circles intersect.

**Q6: **

In what interval must lie for to be the equation of a circle?

- A
- B
- C
- D

**Q8: **

Given that is a circle, what is its radius?

**Q9: **

Determine the equation of the circle that passes through and and has its centre on the -axis.

- A
- B
- C
- D

**Q10: **

Find the equation of the circle with center which touches the -axis.

- A
- B
- C
- D

**Q11: **

The equation represents a circle, what are and ?

- A ,
- B ,
- C ,
- D ,

**Q12: **

Find the equations of all possible circles that pass through the two points and and have a radius of 5.

- A or
- B or
- C or
- D or

**Q13: **

Does the equation represent a circle?

- Ayes
- Bno

**Q14: **

Does the equation represent a circle?

- Ano
- Byes

**Q15: **

Find all the real values of for which is the equation of a circle.

- A
- B
- C
- D

**Q16: **

The line is tangent to the circle . What is ?

- A5
- B4
- C
- D

**Q17: **

The circle in the figure has equation , and the line is . Find the length of to the nearest hundredth.

**Q18: **

Consider a circle centered at passing through the origin.

Write the equation of the circle.

- A
- B
- C
- D
- E

The circle is dilated by a scale factor of two such that the circle still passes through the origin. Write the equation of the circle.

- A
- B
- C
- D
- E

What is the radius of the new circle?

- A
- B4
- C
- D8
- E2

**Q19: **

Are the two circles expressed by the equations and congruent?

- Ano
- Byes

**Q20: **

Find the centre and radius of the circle .

- A centre: , radius:
- B centre: , radius:
- C centre: , radius:
- D centre: , radius:
- Ecentre: , radius: