Question

The eccentricity of the ellipse \[ 16x^2+7y^2=112 \] is

• A. \(\frac{4}{3}\)
• B. \(\frac{7}{16}\)
• C. \(\frac{3}{\sqrt7}\)
• D. \(\frac{3}{4}\)

Hint:

For ellipse, always identify the larger denominator as \(a^2\).

Answer 1

The Correct Option is D

Step 1: Given ellipse: \[ 16x^2+7y^2=112 \]

Step 2: Divide by \(112\): \[ \frac{x^2}{7}+\frac{y^2}{16}=1 \]

Step 3: Here larger denominator is \(16\), so: \[ a^2=16,\qquad b^2=7 \]

Step 4: Eccentricity: \[ e=\sqrt{1-\frac{b^2}{a^2}} \] \[ e=\sqrt{1-\frac{7}{16}} \] \[ e=\sqrt{\frac{9}{16}} \] \[ e=\frac{3}{4} \] \[ \boxed{\frac{3}{4}} \]