Question

What is the equation of the circle with center (0, 1) and a radius of 10?

Answer 1

The equation of the circle with center (0, 1) and a radius of 10 is
`\bold{x^(2) + y^(2) - 2y-99 = 0}`

Solution:

Equation of circle whose center (h, k) and radius r is given as,

`(x-h)^(2) + (y-k)^(2) = r^(2)` ---- eqn 1

From question, given that the circle has radius 10 and center (0, 1). We have to find the equation of the circle.

Hence we get, h = 0 ; k = 1; r = 10

By using eqn 1, the equation of circle whose center (0, 1) and radius 10 is given as

`(x-0)^(2) + (y - 1)^(2) = 10^(2)`

On Simplifying we get

`x^(2) + (y-1)^(2) = 10^(2)`

Expand
`(y-1)^(2)` using the formula
`(a-b)^(2) = a^(2) - 2ab + b^(2)`

`x^(2) + y^(2) - 2y + 1 = 10^(2)`

`x^(2) + y^(2) - 2y + 1 = 100`

`x^(2) + y^(2) - 2y + 1-100 = 0`

`x^(2) + y^(2)- 2y- 99 = 0`

Hence equation of the circle with center (0, 1) and a radius of 10 is
`\bold{x^(2)+y^(2)-2 y-99=0}`