Question

For the ellipse \[\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\], which expression for \[y\] is obtained before selecting the first-quadrant branch?

Options

• \[y=\pm\frac{a}{b}\sqrt{b^2-x^2}\]

• \[y=\pm\frac{b}{a}\sqrt{a^2-x^2}\]

• \[y=\frac{b}{a}(a^2-x^2)\]

• \[y=\pm\frac{b}{a}\sqrt{x^2-a^2}\]

Answer 1

Rearranging the ellipse equation gives \[y^2=\frac{b^2}{a^2}(a^2-x^2)\]. Taking square roots gives the two branches \[y=\pm\frac{b}{a}\sqrt{a^2-x^2}\].