Answer:
The correct option is 1.
Step-by-step explanation:
The given function is
[tex]36x^2+49y^2=1764[/tex]
Divide both sides by 1764,
[tex]\frac{x^2}{49}+\frac{y^2}{36}=1[/tex] .... (1)
The standard form of ellipse is
[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex] .... (2)
The focus of this equation is [tex](\pm c,0)[/tex].
where, [tex]c^2=a^2-b^2[/tex]
On comparing (1) and (2), we get
[tex]a^2=49, b^2=36[/tex]
[tex]c^2=a^2-b^2[/tex]
[tex]c^2=49-36[/tex]
[tex]c^2=13[/tex]
[tex]c=\pm\sqrt{13}[/tex]
Therefore the foci of the given ellipse are (-√13, 0) and (√13,0). Option 1 is correct.
