Hhhhhelp plzzz look at the photo answer all three if possible

QUESTION 1

Given foci to be

[tex](\pm1,0)[/tex]

[tex]c = \pm1[/tex]

and

co-vertices

[tex](0, \pm2)[/tex]

[tex]b = \pm \: 2[/tex]

[tex] {b}^{2} = 4[/tex]

This implies the minor axis of the ellipse is on the y-axis and the major axis is on the x-axis.

We use the equation

[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]

to determine the vertices.

[tex] {a}^{2} - {( \pm2)}^{2} = { ( \pm1)}^{2} [/tex]

[tex] {a}^{2} - 4 = 1[/tex]

[tex] {a}^{2} = 5[/tex]

The equation of the ellipse is given by;

[tex] \frac{ {x}^{2} }{ {a}^{2} } + \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

[tex] \frac{ {x}^{2} }{ 5} + \frac{ {y}^{2} }{4} = 1[/tex]

QUESTION 2

The given ellipse has

Foci

[tex](0,\pm2)[/tex]

[tex]c = \pm2[/tex]

and co-vertices,

[tex](\pm1,0)[/tex]

[tex]b = \pm1[/tex]

[tex] {b}^{2} = 1[/tex]

We use the equation,

[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]

to determine the vertices.

[tex]{a}^{2} - { (\pm1)}^{2} = {( \pm2)}^{2} [/tex]

[tex]{a}^{2} - 1= 4[/tex]

[tex]{a}^{2} =5[/tex]

The major axis of the ellipse is on the y-axis this time.

The equation is given by;

[tex] \frac{ {x}^{2} }{ {b}^{2} } + \frac{ {y}^{2} }{ {a}^{2} } = 1[/tex]

[tex]\frac{ {x}^{2} }{ 4} + \frac{ {y}^{2} }{ 5} = 1[/tex]

QUESTION 3

The given ellipse has

Foci

[tex](0,\pm4)[/tex]

and co-vertices,

[tex](\pm4,0)[/tex]

[tex]b = \pm4[/tex]

[tex] {b}^{2} = 16[/tex]

[tex]{a}^{2} - {b}^{2} = {c}^{2} [/tex]

[tex]{a}^{2} - 16= 16[/tex]

[tex]{a}^{2} = 32[/tex]

The major axis is on the y-axis.

The equation is,

[tex]\frac{ {x}^{2} }{ {b}^{2} } + \frac{ {y}^{2} }{ {a}^{2} } = 1[/tex]

[tex]\frac{ {x}^{2} }{16} + \frac{ {y}^{2} }{32 } = 1[/tex]