Question

The eccentricity of the ellipse given by the equation \[ 9x^2 + 16y^2 = 144 \] is

• A. \(\dfrac{\sqrt{7}}{4}\)
• B. \(\dfrac{1}{4}\)
• C. \(\dfrac{\sqrt{3}}{4}\)
• D. \(\dfrac{\sqrt{5}}{4}\)

Hint:

Always reduce the ellipse equation to standard form before identifying \(a\) and \(b\).

Answer 1

The Correct Option is A

Step 1: Write the equation in standard form.
\[ \frac{x^2}{16} + \frac{y^2}{9} = 1 \] 
Step 2: Identify \(a^2\) and \(b^2\). 
Here \(a^2 = 16\), \(b^2 = 9\) with \(a>b\). 

Step 3: Use the eccentricity formula. 
\[ e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{9}{16}} = \sqrt{\frac{7}{16}} = \frac{\sqrt{7}}{4} \]