Question Video: Finding the Equation of a Sphere given Its Radius and the Coordinates of Its Centre | Nagwa Question Video: Finding the Equation of a Sphere given Its Radius and the Coordinates of Its Centre | Nagwa

# Question Video: Finding the Equation of a Sphere given Its Radius and the Coordinates of Its Centre Mathematics • Third Year of Secondary School

## Join Nagwa Classes

Attend live Mathematics sessions on Nagwa Classes to learn more about this topic from an expert teacher!

Give the equation of the sphere of center (11, 8, β5) and radius 3 in standard form.

01:51

### Video Transcript

Give the equation of the sphere of center 11, eight, negative five and radius three in standard form.

Letβs recall first of all what is meant by the standard form of the equation of a sphere. If a sphere has its center at the point with coordinates π, π, π and a radius of π units, then the equation of that sphere in standard form is given by π₯ minus π squared plus π¦ minus π squared plus π§ minus π squared is equal to π squared, where π₯, π¦, π§ are the coordinates of any point on the surface of the sphere.

Weβve been given both the center and radius of our sphere. So we can substitute the values of π, π, π, and π into the standard form. We get π₯ minus 11 squared plus π¦ minus eight squared plus π§ minus negative five squared is equal to three squared.

Be careful here. A common mistake would be to forget one of the minus signs and write down just π§ minus five squared. But weβre subtracting negative five. So we must write π§ minus negative five squared. We can of course simplify this though because the two negative signs together will form a positive. π§ minus negative five is equal to π§ plus five. So we can replace that third bracket with π§ plus five squared. On the right-hand side of our equation, three squared is equal to nine.

So the equation of the sphere of center 11, eight, negative five and radius three in standard form is π₯ minus 11 squared plus π¦ minus eight squared plus π§ plus five squared is equal to nine. If we were asked to give the equation in expanded form, weβd need to expand each of the brackets and then simplify the result by collecting like terms.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy