Question

Why is \[y\] taken as positive for the region AOBA of the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\]?

Options

• The ellipse is symmetrical only about the \[x\]-axis.

• The region AOBA lies in the first quadrant.

• The ordinate is \[x=0\].

• The region AOBA lies below the \[x\]-axis.

Answer 1

The first quadrant has positive \[y\]-coordinates. Therefore the positive branch \[y=\frac{b}{a}\sqrt{a^2-x^2}\] is used for region AOBA.