**Q1: **

Find the equation of a sphere that passes through the points , , and , given that its center lies on the -plane.

- A
- B
- C
- D

**Q2: **

A sphere is tangent to the -plane, and has its center on the -axis at a distance of 35 length units from the -plane. What is the equation of the sphere?

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

**Q3: **

The spheres with equations and intersect in a circle. Find the equation of the plane in which this circle lies.

- A
- B
- C
- D
- E

**Q4: **

Find the point(s) of intersection of the sphere and the line , , .

- A ,
- B
- C
- Dno intersection point
- E ,

**Q5: **

Determine if the given equation describes a sphere. If so, find its radius and center.

- AYes, it describes a sphere of radius 1 centered at .
- BYes, it describes a sphere of radius 1 centered at .
- CYes, it describes a sphere of radius 3 centered at .
- DNo, it does not describe a sphere.
- EYes, it describes a sphere of radius 2 centered at .

**Q6: **

Give the equation of the sphere of center and radius 3 in standard form.

- A
- B
- C
- D

**Q7: **

The line is tangent to the sphere . Find the sphereβs radius to the nearest hundredth.

**Q8: **

Does the given equation describe a sphere? If so, find its radius and center.

- Ayes, it describes a sphere. Its radius is 5 and its center is at .
- Bno, it does not describe a sphere.
- Cyes, it describes a sphere. Its radius is 11 and its center is at .
- Dyes, it describes a sphere. Its radius is 5 and its center is at .
- Eyes, it describes a sphere. Its radius is 11 and its center is at .

**Q9: **

Which of the following does the equation represent?

- Aa circle of radius length units
- Ba circle of radius 3 length units
- Ca sphere of radius length units
- Da sphere of radius 3 length units
- Ea plane

**Q10: **

It can be shown that any four noncoplanar points determine a sphere. Find the equation of the sphere that passes through the points , , and .

- A
- B
- C
- D
- E

**Q11: **

Determine if the given equation describes a sphere. If so, find its radius and center.

- AYes, it describes a sphere. Its radius is 1 and its center is at .
- BYes, it describes a sphere. Its radius is 1 and its center is at .
- CYes, it describes a sphere. Its radius is 2 and its center is at .
- DNo, it does not describe a sphere.
- EYes, it describes a sphere. Its radius is 2 and its center is at .

**Q12: **

Which of the following is the equation of a sphere of the center and passing through ?

- A
- B
- C
- D

**Q13: **

Determine the equation of a sphere with center , given that it touches one of coordinate planes.

- A
- B
- C
- D

**Q14: **

Given that a sphereβs equation is , determine its center and radius.

- A , 289 length units
- B , 289 length units
- C , 17 length units
- D , 17 length units

**Q15: **

A sphere of radius 2 is tangent to all three coordinate planes. Given that the coordinates of its center are all positive, what is the equation of this sphere?

- A
- B
- C
- D

**Q16: **

Determine the surface area of the sphere of equation , leaving your answer in terms of .

- A
- B
- C
- D

**Q17: **

Determine if the given equation describes a sphere. If so, find its radius and center.

- AYes, it describes a sphere. Its radius is 1 and its center is at .
- BNo, it does not describe a sphere.
- CYes, it describes a sphere. Its radius is 5 and its center is at .
- DYes, it describes a sphere. Its radius is 1 and its center is at .
- EYes, it describes a sphere. Its radius is 5 and its center is at .

**Q18: **

Given , and that is a diameter of the sphere , what is the point ?

- A
- B
- C
- D

**Q19: **

Find the equation of the sphere concentric with , but with twice the radius.

- A
- B
- C
- D