write the equation of an ellipse centered at the origin that has a horizontal major axis, e=1/2, and 2c=1

Question

how do I solve this, write an equation of an ellipse center at the origin that has a horizontal major axis,e=1/2,and 2c=1

Answer 1

h = k = 0

 

2c = 1

c = 1/2

 

e = c/a

1/2 = 1/2a

a = 1

 

c² = a² - b²

1/4 = 1 - b²

b² = 3/4

 

x² + 4y²/3 = 1