Question

Comprueba que la ecuación de la circunferencia 4x²+4y²-8x+16y-5 = 0

Answer 1

Respuesta:

$4x^2+4y^2-8x+16y-5 = 0\\\\4x^2-8x+4y^2+16y-5 = 0\\\\4(x^2-2x)+4(y^2+4y)-5=0\\\\4(x^2-2x+1-1)+4(y^2+4y+4-4)-5=0\\\\4((x-1)^2-1)+4((y+2)^2-4)-5=0\\\\4(x-1)^2-4+4(y+2)^2-16-5=0\\\\4(x-1)^2+4(y+2)^2-25=0\\\\4(x-1)^2+4(y+2)^2=25\\\\4[(x-1)^2+(y+2)^2]=25\\\\(x-1)^2+(y+2)^2=\frac{25}{4} \\\\(x-1)^2+(y+2)^2=(\frac{5}{2} )^2\\\\\\Lo\ cual\ demuestra\ que\ es\ la\ ecuacion\\ de\ una\ circunferencia\ con\ centro\ en\ (1,-2)\ y\ radio\ 5/2$