Question

Length of latusrectum of the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,\] is______.

Options

• \[\frac{2a^{2}}{b},\mathrm{if}a<b\]

• \[\frac{2a^{2}}{b},\mathrm{if}a>b\]

• \[\frac{2b^{2}}{a},\mathrm{if}a<b\]

• None of these

Answer 1

Length of latusrectum of the ellipse \[\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,\] is \[\frac{2b^{2}}{a},\mathrm{if}a<b\].

Explanation:

If a > b, then length of the latusrectum is \[\frac{2b^2}{a}\] when a < b, then length of the latusrectum is \[\frac{2a^2}{b}\].