Answer:
D, 4.62
Step-by-step explanation:
e = √(1 - b²/a²)
To solve for a, first square both sides:
e² = 1 - b²/a²
Then subtract 1 from both sides:
e² - 1 = -b²/a²
Multiply both sides by -1:
1 - e² = b²/a²
Multiply by a²:
(1 - e²) a² = b²
Divide by 1 - e²:
a² = b² / (1 - e²)
Take the square root:
a = b / √(1 - e²)
So the answer is D.
When b = 4 and e = ½:
a = 4 / √(1 - (½)²)
a = 4 / √(1 - ¼)
a = 4 / √¾
a = 8 / √3
a ≈ 4.62
