Worksheet: Application of Equations of Circles

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

Q1:

By completing the square, find the centre and radius of the circle .

• A centre: , radius: 4
• B centre: , radius: 16
• C centre: , radius: 4
• D centre: , radius: 4

Q2:

The equation describes a circle. Find its center and radius.

• A
• B
• C
• D

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

Q7:

Given and , determine the equation of the circle for which is a diameter.

• 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 .