Find the eccentricity of the ellipse x^218+y^2/8=1.

Find the eccentricity of the ellipse $\frac{x ^{2}}{18} + \frac{y ^{2}}{8} = 1$ .

easy 2 marks Class 11 · Mathematics · Conic Sections

Answer

\frac{5}{3}

The correct answer is $\frac{5}{3}$ — Substitute the values to get $e = 1 - \frac{8}{18} = 1 - \frac{4}{9} = \frac{5}{9} = \frac{5}{3}$ .

Identify $a^{2}$ and $b^{2}$ from the standard form $\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1$ ; here $a^{2} = 18$ and $b^{2} = 8$ because $18 > 8$ .
Use the formula for eccentricity of an ellipse: $e = 1 - \frac{b ^{2}}{a ^{2}}$ .
Substitute the values to get $e = 1 - \frac{8}{18} = 1 - \frac{4}{9} = \frac{5}{9} = \frac{5}{3}$ .

Common mistake: Using

e = 1 - \frac{a ^{2}}{b ^{2}}

or misidentifying which denominator is

a^{2}

Concept tested: Eccentricity of an ellipse