Correct Answer - Option 3 :
\(\rm \frac{x^2}{16}+\frac{y^2}{12}=1\)
Concept:
Equation of ellipse: \(\rm \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)
Foci: (±ae, 0)
Eccentricity, e = \(\rm \sqrt{1-\frac{b^2}{a^2}}\)
Calculation:
Here,foci = (±2,0) = (±ae, 0) and the eccentricity, e = 1/2
ae = 2
⇒ a × 1/2 = 2
⇒ a = 4
⇒ a2 = 16
Now, e = \(\rm \sqrt{1-\frac{b^2}{a^2}}\)
⇒ b2= a2(1 - e2)
= 16(1 - 1/4)
= 16× (3/4)
= 12
∴ Equation of ellipse = \(\rm \frac{x^2}{16}+\frac{y^2}{12}=1\)
Hence, option (3) is correct.