Question

26) O raio da circunferência x2 + y2 + 22x – 24y + 252 = 0 é igual a:
a)
1
b)
13
c)
$\sqrt{13}$
d)
5
e)
25

Answer 1

$\boxed{\boxed{c) \ \sqrt{13}}}\\\\\\x^2 + y^2 - 2ax - 2by + a^2 + b^2 - r^2 = 0\\\\x^2 + y^2 + 22x - 24y + 252 = 0\\\\-2a = 22\\a = -\dfrac{22}{2}\\a=-11\\\\-2b = -24\\b = \dfrac{24}{2}\\b = 12\\\\a^2 + b^2 - r^2 = 252\\(-11)^2 + 12^2 - r^2 = 252\\121 + 144 - r^2 = 252\\265 - r^2 = 252\\r^2 = 265 - 252\\r^2 = 13\\r = \sqrt{13}$