Question

ecuación canónica x2+4y2-4x-8y-95=0​

Answer 1

${x}^{2} + {y}^{2} + dx + ey + f = 0$

la ecuación

${x}^{2} + {y}^{2} - 4x - 8y- 95 = 0$

el centro

$c = ( \frac{ - d}{2} \: \: \frac{ - e}{2}) \\ c = ( \frac{4}{2} \: \: \: \frac{8}{2} ) \\ c = (2 \: \: \: 4)$

radio

$r = \frac{1}{2} \sqrt{ {d}^{2} + {e}^{2} - 4f } \\ r = 0.5 \sqrt{16 + 64 + 380} \\ r = 0.5 \sqrt{460} \\ r= 10.72$

ecuación canónica

$( x - h)^{2} + ( y - k) ^{2} = r^{2} \\ (x - 2) ^{2} + (y - 4)^{2} = 10.72^{2} \\ (x - 2) ^{2} + (y - 4)^{2} = 114.91$