Instrucciones: Responde las siguientes preguntas.

• Transforma la ecuación de elipse \(\displaystyle{\frac{\left ( x+6 \right )^{2}}{81}+\frac{\left ( y+20 \right )^{2}}{289} = 1}\) a su forma general.
  • $$289x^{2}+81y^{2}-4 \ 845x-4 \ 780y+7 \ 795 = 0$$
  • $$289x^{2}+81y^{2}+3 \ 468x+3 \ 240y+29 \ 305 = 0$$
  • $$289x^{2}+81y^{2}-4 \ 845x-4 \ 780y+8 \ 500 = 0$$
  • $$289x^{2}+81y^{2}+3 \ 468x+3 \ 240y+19 \ 395 = 0$$

• Transforma la ecuación de elipse \(\displaystyle{\frac{\left ( x+5 \right )^{2}}{196}+\frac{\left ( y+6 \right )^{2}}{9} = 1}\) a su forma general.
  • $$9x^{2}+196y^{2}-175x-1 \ 341y-9 \ 759 = 0$$
  • $$9x^{2}+196y^{2}+90x+2 \ 352y-5 \ 765 = 0$$
  • $$9x^{2}+196y^{2}+90x+2 \ 352y+5 \ 517 = 0$$
  • $$9x^{2}+196y^{2}-175x-1 \ 341y+2 \ 109 = 0$$

• Transforma la ecuación de elipse \(\displaystyle{\frac{\left ( x+2 \right )^{2}}{49}+\frac{\left ( y-8 \right )^{2}}{100} = 1}\) a su forma general.
  • $$100x^{2}+49y^{2}+400x-784y-1 \ 364 = 0$$
  • $$100x^{2}+49y^{2}-360x+420y-2 \ 492 = 0$$
  • $$100x^{2}+49y^{2}-360x+420y-1 \ 924 = 0$$
  • $$100x^{2}+49y^{2}+400x-784y-456 = 0$$

• Transforma la ecuación de elipse \(\displaystyle{\frac{\left ( x-20 \right )^{2}}{324}+\frac{\left ( y-9 \right )^{2}}{64} = 1}\) a su forma general.
  • $$16x^{2}+81y^{2}-640x-1 \ 458y+479 = 0$$
  • $$16x^{2}+81y^{2}-640x-1 \ 458y+7 \ 777 = 0$$
  • $$16x^{2}+36y^{2}+910x+397y+9 \ 772 = 0$$
  • $$16x^{2}+36y^{2}+910x+397y-4 \ 107 = 0$$

• Transforma la ecuación de elipse \(\displaystyle{\frac{\left ( x-3 \right )^{2}}{25}+\frac{\left ( y-1 \right )^{2}}{64} = 1}\) a su forma general.
  • $$64x^{2}+25y^{2}-384x-50y-999 = 0$$
  • $$64x^{2}+25y^{2}-384x-50y-1 \ 381 = 0$$
  • $$64x^{2}+25y^{2}-387x-40y-1 \ 903 = 0$$
  • $$64x^{2}+25y^{2}-387x-40y-1 \ 057 = 0$$