Question

Help me fast please

give the coordinates(enclose the coordinates in parentheses) of the
foci,vertices,and convertices of the ellipse with equation x²/169 + y²/25 = 1​

Answer 1

`(x^2)/(169) +(y^2)/(25)=1`

If we compare this to the general expression for an ellipse given by:

`((x-h)^2)/(a^2) +((y-k)^2)/(b^2)=1`

We can see that the vertex is
`V=(0,0)`

And we can find the values of a and b like this:

`a=√(169)=13, b=√(25)=5`

in order to find the foci we can find the value of c

`c =√(169-25)=√(144)=12`

The two focis are (12,0) and (-12,0)

The convertices for this case are: (13,0) and (-13,0) on the x axis

And for the y axis (0,5) and (0,-5)

Explanation:

For this problem we have the following equation given:

`(x^2)/(169) +(y^2)/(25)=1`

If we compare this to the general expression for an ellipse given by:

`((x-h)^2)/(a^2) +((y-k)^2)/(b^2)=1`

We can see that the vertex is
`V=(0,0)`

And we can find the values of a and b like this:

`a=√(169)=13, b=√(25)=5`

in order to find the foci we can find the value of c

`c =√(169-25)=√(144)=12`

The two focis are (12,0) and (-12,0)

The convertices for this case are: (13,0) and (-13,0) on the x axis

And for the y axis (0,5) and (0,-5)