Answer:
3√2
Step-by-step 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
Answer:
[tex]3\sqrt{2}[/tex] units
Step-by-step explanation:
Convert general form to standard form:
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex]
[tex]1x^2+0xy+1y^2-4x-4y-10=0[/tex] (Since [tex]A=C[/tex], the conic section is a circle)
[tex]x^2+y^2-4x-4y-10=0[/tex]
[tex]x^2-4x+y^2-4y-10=0[/tex]
[tex]x^2-4x+y^2-4y=10[/tex]
[tex]x^2-4x+4+y^2-4y+4=10+4+4[/tex]
[tex](x-2)^2+(y-2)^2=18[/tex]
Since we have our equation in standard form, we can see that the radius is [tex]\sqrt{18}=3\sqrt{2}[/tex] units
