Answer:
1. [tex]F_1(0,-\sqrt{35}),\ F_2(0,\sqrt{35}).[/tex]
2. [tex]F_1(0,-\sqrt{12}),\ F_2(0,\sqrt{12}).[/tex]
3. [tex]F_1(-\sqrt{5},0),\ F_2(\sqrt{5},0).[/tex]
Step-by-step explanation:
The foci of ellipse have the coordinates [tex]F_1(-c,0),\ F_2(c,0),[/tex] where [tex]c=\sqrt{a^2-b^2}[/tex] if a>b and [tex]F_1(0,-c),\ F_2(0,c),[/tex] where [tex]c=\sqrt{b^2-a^2}[/tex] if b>a.
1. [tex]a=1,\\ \\b=6,\\ \\c=\sqrt{36-1}=\sqrt{35}[/tex]
and foci are on y-axis [tex]F_1(0,-\sqrt{35}),\ F_2(0,\sqrt{35}).[/tex]
2. [tex]a=2,\\ \\b=4,\\ \\c=\sqrt{16-4}=\sqrt{12}[/tex]
and foci are on y-axis [tex]F_1(0,-\sqrt{12}),\ F_2(0,\sqrt{12}).[/tex]
3. [tex]a=3,\\ \\b=2,\\ \\c=\sqrt{9-4}=\sqrt{5}[/tex]
and foci are on x-axis [tex]F_1(-\sqrt{5},0),\ F_2(\sqrt{5},0).[/tex]
