Question

What’s the radius of x^2+y^2-4x-4y-10=0

Answer 1

`3√(2)` units

Explanation:

Convert general form to standard form:

`Ax^2+Bxy+Cy^2+Dx+Ey+F=0`

`1x^2+0xy+1y^2-4x-4y-10=0` (Since
`A=C`, the conic section is a circle)

`x^2+y^2-4x-4y-10=0`

`x^2-4x+y^2-4y-10=0`

`x^2-4x+y^2-4y=10`

`x^2-4x+4+y^2-4y+4=10+4+4`

`(x-2)^2+(y-2)^2=18`

Since we have our equation in standard form, we can see that the radius is
`√(18)=3√(2)` units

Answer 2

3√2

Explanation:

x² + y² - 4x - 4y - 10 = 0

We need to complete the square in x and y.

x² - 4x + y² - 4y = 10

x² - 4x + 4 + y² - 4y + 4 = 10 + 4 + 4

(x - 2)² + (y - 2)² = 18

(x - 2)² + (y - 2)² = (3√2)²

Compare to:

(x - h)² + (y - k)² = r²

We have:

r = 3√2