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 \\\\ (4x^2)/(100)+ (25y^2)/(100)= (100)/(100) \\\\ (x^2)/(25)+ (y^2)/(4)= 1 \\\\ (x^2)/(5^2)+ (y^2)/(2^2)= 1 \\\\ This \;is \;an \;ellipse. \\\\ </p><p>(x^2)/(a^2)+ (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].