From the given equation, foci of ellipse are [tex](0,\± 3)[/tex].
What is ellipse?
" Ellipse is defined as the closed curve in a plane whose distance from a two fixed point has constant value."
Formula used
Equation of the ellipse
[tex]\frac{x^{2} }{b^{2} } +\frac{y^{2} }{a^{2} } =1[/tex]
Foci of ellipse [tex]=( 0, \± c)[/tex]
According to the question,
Given equation of ellipse,
[tex]25x^{2} +16y^{2} =400[/tex]
Divide both the side by [tex]400[/tex] we get,
[tex]\frac{25x^{2} }{400} +\frac{16y^{2} }{400} =\frac{400}{400} \\\\\frac{x^{2} }{16}+\frac{y^{2} }{25} =1[/tex]
Compare it with general equation of ellipse we have,
[tex]a > b[/tex]
[tex]a = 5 , \\\\b = 4[/tex]
Distance between focus and center of the ellipse we get,
[tex]c^{2} =a^{2} -b^{2}\\\\\implies c^{2} = 25 -16\\\\\implies c^{2} = 9\\\\\implies c = \±3[/tex]
Hence, for the given equation foci of ellipse are [tex](0,\± 3)[/tex].
Learn more about ellipse here
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