# Worksheet: Equations of Circles Using Tangents

In this worksheet, we will practice finding the equation of a circle using tangents.

**Q1: **

Determine the equation of a circle whose radius equals 8 length units and center lies in the first quadrant, given that the two straight lines and are two tangents to the circle.

- A
- B
- C
- D

**Q2: **

If the -axis is a tangent to a circle whose equation is , find all possible values of .

- A or
- B
- C or
- D or

**Q3: **

Find the general form of the equation of a circle that is tangent to the -axis and has center .

- A
- B
- C
- D

**Q4: **

Pulley is attached by a wire cable to pulley , which is tangent to both coordinate axes and has radius 5. What is the equation of this circle?

- A
- B
- C
- D

**Q5: **

A circle is in the third quadrant and touches the -axis at . If it is also tangent to the -axis, what is the equation of the circle?

- A
- B
- C
- D

**Q6: **

Give the equations of all circles tangent to the coordinate axes and passing through .

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

**Q7: **

Determine the equation of a circle with center and tangent to the line .

- A
- B
- C
- D

**Q8: **

Circle in the figure is tangent to the axes at points and , and also tangent to the line at . Find the equation of the circle.

- A
- B
- C
- D

**Q9: **

Find the general form of the equation of a circle that passes through the two points and , given that the tangents at and are parallel.

- A
- B
- C
- D

**Q10: **

The -axis is tangent to the circle . What are the possible values of ?

- A12
- B7
- C
- D

**Q11: **

Determine the general form of the equation of circle , given that it touches the two lines and and that the straight line passes through its center.

- A
- B
- C
- D

**Q12: **

Find the general equation of the circle , given that it touches the -axis at and the straight line at .

- A
- B
- C
- D

**Q13: **

Determine the equation of the circle having its center at point and touching the straight line passing through the two points and .

- A
- B
- C
- D

**Q14: **

Are the two circles and externally tangent?

- Ano
- Byes

**Q15: **

Given that the two straight lines and are tangent to a circle, determine its radius.

**Q16: **

Circles and have a common tangent. What are the possible values of ?

- A28 or 48
- B25 or 625
- C14 or 24
- D196 or 576

**Q17: **

The straight line touches the circle at and intersects the -axis at . Determine the equation of the circle .

- A
- B
- C
- D