4x^2+25y^2=100
[tex]4x^2+25y^2=100 \\\\
Dividing \;both \;sides \;by \;100 \\\\
\frac{4x^2}{100}+ \frac{25y^2}{100}= \frac{100}{100} \\\\
\frac{x^2}{25}+ \frac{y^2}{4}= 1 \\\\
\frac{x^2}{5^2}+ \frac{y^2}{2^2}= 1 \\\\
This \;is \;an \;ellipse. \\\\
\frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1 [/tex]
Domain of an ellipse is x ∈ [-a,a] and Range of an ellipse is y ∈ [-b,b].
So, given equation is an Ellipse where Domain is x ∈ [-5,5] and Range is y ∈ [-2,2].
