# Worksheet: Finding the Equation of a Circle 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 or
• C
• 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 ?

• A7
• B12
• 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?

• Ayes
• Bno

Q15:

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

• A2 length units
• B10 length units
• C7 length units
• D1 length unit

Q16:

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

• A28 or 48
• B196 or 576
• C14 or 24
• D25 or 625

Q17:

The straight line touches the circle at and intersects the -axis at . Determine the equation of the circle . • A
• B
• C
• D