# Worksheet: Equation of a Circle with a Center and a Point

In this worksheet, we will practice finding the equation of a circle using its center and a given point.

**Q5: **

A circle has centre and goes through the point . Find the equation of the circle.

- A
- B
- C
- D
- E

**Q6: **

A circle centered at the origin goes through the point (1, 1).

Work out the equation of the circle.

- A
- B
- C
- D
- E

Determine the positive value of when .

- A
- B
- C
- D
- E

Is the point on the circle?

- ANo
- BYes

**Q7: **

Determine the equation of a circle whose centre is at the point , given that the circle touches the straight line .

- A
- B
- C
- D

**Q8: **

The given figure shows a circle with center and a point lying on the circumference of the circle.

Find the length of in terms of and .

- A
- B
- C
- D
- E

Find the length of in terms of and .

- A
- B
- C
- D
- E

Using the Pythagorean Theorem, express in terms of the lengths of and .

- A
- B
- C
- D
- E

**Q9: **

Find the radius of the circle that passes through point and has centre .

- A
- B
- C
- D
- E21

**Q10: **

Does the coordinate lie on the circle centred at the point passing through the point ?

- A We need more information in order to work it out.
- B no
- C yes