Question

36x2 + 49y2 = 1,764 The foci are located at: (-√13, 0) and (√13,0) (0, -√13) and (0,√13) (-1, 0) and (1, 0)

Edit: The answer is (- the square root of 13, 0) and (the square root of 13, 0)

Answer 1

The correct option is 1.

Explanation:

The given function is

`36x^2+49y^2=1764`

Divide both sides by 1764,

`(x^2)/(49)+(y^2)/(36)=1` .... (1)

The standard form of ellipse is

`(x^2)/(a^2)+(y^2)/(b^2)=1` .... (2)

The focus of this equation is
`(\pm c,0)`.

where,
`c^2=a^2-b^2`

On comparing (1) and (2), we get

`a^2=49, b^2=36`

`c^2=a^2-b^2`

`c^2=49-36`

`c^2=13`

`c=\pm√(13)`

Therefore the foci of the given ellipse are (-√13, 0) and (√13,0). Option 1 is correct.