Question

Calcular la longitud de la circunferencia cuya ecuacion es:

x² + y² - 6x +2y -15 = 0

la rpta es 10 π

Answer 1

$x^2+y^2-6x+2y-15=0$
$x^2-6x+2y+y^2=15$
$\left(x^2-6x\right)+\left(y^2+2y\right)=15$
$\left(x^2-6x+9\right)+\left(y^2+2y\right)=15+9$
$\left(x-3\right)^2+\left(y^2+2y\right)=15+9$
$\left(x-3\right)^2+\left(y^2+2y+1\right)=15+9+1$
$\left(x-3\right)^2+\left(y+1\right)^2=15+9+1$
$\left(x-3\right)^2+\left(y+1\right)^2=25$
$\left(x-3\right)^2+\left(y-\left(-1\right)\right)^2=5^2$

$\left(a,\:b\right)=\left(3,\:-1\right),\:r=5$

$P = 2\pi r = 2 \pi 5 = 10 \pi = 31.41592$