Question

The equation x^2 + y^2 + 21 = 40 + 18y. What is the radius of this cookie?​

Answer 1

The radius is 10

Explanation:

Given

`x^2 + y^2 + 21 = 40 + 18y.`

Required

The radius

Rewrite as:

`x^2 + y^2 - 18y = 40-21`

Subtract 81 from both sides

`x^2 + y^2 - 18y +81= 40-21+81`

Expand

`x^2 + y^2 - 9y - 9y +81= 40-21+81`

Factorize

`x^2 + y( y- 9) - 9(y -9)= 40-21+81`

Factor out y - 9

`x^2 + (y- 9) (y -9)= 40-21+81`

Express as squares

`x^2 + (y- 9)^2= 100`

`x^2 + (y- 9)= 10^2`

The equation of a circle is:

`(x - a)^2 + (y- b)= r^2`

By comparison:

`r^2=10^2`

`r = 10`