Correct Answer – Option 4 : 12

Concept:

The standard equation of an ellipse:

\(\rm {x^2\over a^2}+{y^2\over b^2} = 1\)

Where 2a and 2b are the length of the major axis and minor axis respectively and center (0, 0)

The eccentricity = \(\rm \sqrt{(a^2-b^2)}\over a\)

Length of latus recta = \(\rm 2b^2 \over a\)

Distance from center to focus = \(\rm \sqrt{a^2-b^2}\)

Calculation:

Given ellipse \(\rm {x^2\over100}+{y^2\over64} = 1\)

The eccentricity (e)

⇒ e = \(\rm \sqrt{100-64}\over 10\)

⇒ e = \(\rm \sqrt{36}\over 10\)

⇒ e = 0.6

Now distance between foci = 2ae

= 2 × 10 × 0.6

∴ Distance between foci = 12