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
