Question

Find the equation of the ellipse in standard form whose major axis is 8 and eccentricity is 1/2.

Answer 1

Answer:

Step-by-step explanation:

Given major axis of the ellipse, 2a = 8

=> a = 4

Given eccentricity of the ellipse, e = 1/2.

But we now e = √1-b²/a².

=> e² = 1 - b²/a²

=> b²/a² = 1 - e²

=>  b²/a²  = 3/4

=> b² = 3/4*4²

=> b² = 12

=> b = √12 which is the semi minor axis.

Equation of the ellipse in standard form is given by

x²/a² + y²/b² =1,

Thus,

x²/16 + y²/12 =1 is the equation.