Question

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

Answer 1

Answer:

The radius is 10

Step-by-step 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:

$r^2=10^2$

$r = 10$