Question

identify the type of conic section that has the equation 4x^2+25y^2=100 and identify its domain and range.

Answer 1

4x^2+25y^2=100

$4x^2+25y^2=100 \\\\ Dividing \;both \;sides \;by \;100 \\\\ \frac{4x^2}{100}+ \frac{25y^2}{100}= \frac{100}{100} \\\\ \frac{x^2}{25}+ \frac{y^2}{4}= 1 \\\\ \frac{x^2}{5^2}+ \frac{y^2}{2^2}= 1 \\\\ This \;is \;an \;ellipse. \\\\ \frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1$

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].