Instrucciones: Responde las siguientes preguntas.

• Determina la ecuación ordinaria de la elipse cuyos vértices se encuentran en \(V_{1}\left ( -23, \ -7 \right )\) y \(V_{2}\left ( 5, \ -7 \right )\), y sus focos en \(F_{1}\left ( -14, \ -7 \right )\) y \(F_{2}\left ( -4, \ -7 \right )\).
  • $$\frac{\left ( x+9 \right )^{2}}{196}+\frac{\left ( y+7 \right )^{2}}{171} = 1$$
  • $$\frac{\left ( x-7 \right )^{2}}{49}+\frac{\left ( y+4 \right )^{2}}{7} = 1$$
  • $$\frac{\left ( x+9 \right )^{2}}{25}+\frac{\left ( y+17 \right )^{2}}{4} = 1$$
  • $$\frac{\left ( x-9 \right )^{2}}{144}+\frac{\left ( y+16 \right )^{2}}{58} = 1$$

• Determina la ecuación ordinaria de la elipse cuyos vértices se encuentran en \(V_{1}\left ( 3, \ 26 \right )\) y \(V_{2}\left ( 3, \ -4 \right )\), y sus focos en \(F_{1}\left ( 3, \ 17 \right )\) y \(F_{2}\left ( 3, \ 5 \right )\).
  • $$\frac{\left ( x+4 \right )^{2}}{5}+\frac{\left ( y-17 \right )^{2}}{16} = 1$$
  • $$\frac{\left ( x-3 \right )^{2}}{189}+\frac{\left ( y-11 \right )^{2}}{225} = 1$$
  • $$\frac{\left ( x-11 \right )^{2}}{86}+\frac{\left ( y+14 \right )^{2}}{169} = 1$$
  • $$\frac{\left ( x+7 \right )^{2}}{32}+\frac{y^{2}}{225} = 1$$

• Determina la ecuación ordinaria de la elipse cuyos vértices se encuentran en \(V_{1}\left ( -2, \ 5 \right )\) y \(V_{2}\left ( 26, \ 5 \right )\), y sus focos en \(F_{1}\left ( 8, \ 5 \right )\) y \(F_{2}\left ( 16, \ 5 \right )\).
  • $$\frac{\left ( x-18 \right )^{2}}{361}+\frac{\left ( y-13 \right )^{2}}{164} = 1$$
  • $$\frac{\left ( x-12 \right )^{2}}{196}+\frac{\left ( y-5 \right )^{2}}{180} = 1$$
  • $$\frac{\left ( x-9 \right )^{2}}{64}+\frac{\left ( y+13 \right )^{2}}{10} = 1$$
  • $$\frac{\left ( x-1 \right )^{2}}{289}+\frac{\left ( y-14 \right )^{2}}{26} = 1$$

• Determina la ecuación ordinaria de la elipse cuyos vértices se encuentran en \(V_{1}\left ( 4, \ 33 \right )\) y \(V_{2}\left ( 4, \ -5 \right )\), y sus focos en \(F_{1}\left ( 4, \ 19 \right )\) y \(F_{2}\left ( 4, \ 9 \right )\).
  • $$\frac{\left ( x-9 \right )^{2}}{119}+\frac{\left ( y+5 \right )^{2}}{121} = 1$$
  • $$\frac{\left ( x+10 \right )^{2}}{124}+\frac{\left ( y+3 \right )^{2}}{256} = 1$$
  • $$\frac{\left ( x-4 \right )^{2}}{336}+\frac{\left ( y-14 \right )^{2}}{361} = 1$$
  • $$\frac{\left ( x-4 \right )^{2}}{62}+\frac{\left ( y+2 \right )^{2}}{81} = 1$$

• Determina la ecuación ordinaria de la elipse cuyos vértices se encuentran en \(V_{1}\left ( -4, \ -2 \right )\) y \(V_{2}\left ( 12, \ -2 \right )\), y sus focos en \(F_{1}\left ( -2, \ -2 \right )\) y \(F_{2}\left ( 10, \ -2 \right )\).
  • $$\frac{\left ( x+9 \right )^{2}}{121}+\frac{\left ( y+2 \right )^{2}}{39} = 1$$
  • $$\frac{\left ( x-4 \right )^{2}}{64}+\frac{\left ( y+2 \right )^{2}}{28} = 1$$
  • $$\frac{\left ( x-3 \right )^{2}}{225}+\frac{\left ( y-18 \right )^{2}}{56} = 1$$
  • $$\frac{\left ( x+19 \right )^{2}}{256}+\frac{\left ( y-14 \right )^{2}}{56} = 1$$