Question

Eccentricity of the conic \[16x^2+7y^2=112\] is______.

Options

• \[\frac{3}{\sqrt{7}}\]

• \[\frac{7}{16}\]

• \[\frac{3}{4}\]

• \[\frac{4}{3}\]

Answer 1

Eccentricity of the conic \[16x^2+7y^2=112\] is \[\frac{3}{4}\].

Explanation:

The given conic is: \[16x^2+7y^2=112\]

Dividing both sides by 112:

                                             \[\frac{x^2}{7}+\frac{y^2}{16}=1\]

This is an ellipse with:

• \[a^2=16\to\] major axis along y-axis
• \[b^2=7\to\] minor axis along x-axis

For eccentricity, we need \[c^2=a^2-b^2\mathrm{:}\]

                                                 \[c^2=16-7=9\Rightarrow c=3\]

                                                \[e=\frac{c}{a}=\frac{3}{\sqrt{16}}=\frac{3}{4}\]