Instrucciones: Responde las siguientes preguntas.

• Transforma la ecuación de elipse \(49x^{2}+16y^{2}-392x+192y+576 = 0\) a su forma ordinaria.
  • $$\frac{\left ( x+5 \right )^{2}}{100}+\frac{\left ( y+3 \right )^{2}}{9} = 1$$
  • $$\frac{\left ( x+9 \right )^{2}}{64}+\frac{\left ( y+8 \right )^{2}}{100} = 1$$
  • $$\frac{\left ( x-1 \right )^{2}}{25}+\frac{\left ( y+1 \right )^{2}}{64} = 1$$
  • $$\frac{\left ( x-4 \right )^{2}}{16}+\frac{\left ( y+6 \right )^{2}}{49} = 1$$

• Transforma la ecuación de elipse \(100x^{2}+289y^{2}-1 \ 200x-2 \ 312y-20 \ 676 = 0\) a su forma ordinaria.
  • $$\frac{\left ( x-10 \right )^{2}}{361}+\frac{\left ( y-18 \right )^{2}}{16} = 1$$
  • $$\frac{\left ( x+10 \right )^{2}}{256}+\frac{\left ( y+5 \right )^{2}}{169} = 1$$
  • $$\frac{\left ( x-11 \right )^{2}}{361}+\frac{\left ( y-1 \right )^{2}}{256} = 1$$
  • $$\frac{\left ( x-6 \right )^{2}}{289}+\frac{\left ( y-4 \right )^{2}}{100} = 1$$

• Transforma la ecuación de elipse \(49x^{2}+16y^{2}+882x+640y+9 \ 585 = 0\) a su forma ordinaria.
  • $$\frac{\left ( x+9 \right )^{2}}{16}+\frac{\left ( y+20 \right )^{2}}{49} = 1$$
  • $$\frac{\left ( x-16 \right )^{2}}{25}+\left ( y+5 \right )^{2} = 1$$
  • $$\frac{\left ( x-13 \right )^{2}}{144}+\frac{\left ( y-10 \right )^{2}}{100} = 1$$
  • $$\frac{\left ( x+2 \right )^{2}}{81}+\frac{\left ( y+3 \right )^{2}}{361} = 1$$

• Transforma la ecuación de elipse \(4x^{2}+y^{2}+56x-8y+112 = 0\) a su forma ordinaria.
  • $$\left ( x+10 \right )^{2}+\frac{\left ( y-3 \right )^{2}}{36} = 1$$
  • $$\frac{\left ( x-5 \right )^{2}}{36}+\frac{\left ( y-7 \right )^{2}}{4} = 1$$
  • $$\frac{\left ( x+3 \right )^{2}}{49}+\left ( y+4 \right )^{2} = 1$$
  • $$\frac{\left ( x+7 \right )^{2}}{25}+\frac{\left ( y-4 \right )^{2}}{100} = 1$$

• Transforma la ecuación de elipse \(16x^{2}+169y^{2}-640x+1 \ 352y+6 \ 400 = 0\) a su forma ordinaria.
  • $$\frac{\left ( x+19 \right )^{2}}{9}+\frac{\left ( y+2 \right )^{2}}{25} = 1$$
  • $$\frac{\left ( x+15 \right )^{2}}{36}+\frac{\left ( y+2 \right )^{2}}{121} = 1$$
  • $$\frac{\left ( x-5 \right )^{2}}{256}+\frac{\left ( y+11 \right )^{2}}{81} = 1$$
  • $$\frac{\left ( x-20 \right )^{2}}{169}+\frac{\left ( y+4 \right )^{2}}{16} = 1$$