The eccentricity of an ellipse whose centre is at the origin is ½

• Coordinate Geometry

The eccentricity of an ellipse whose centre is at the origin is ½. If one of its directrices is x = -4, then the equation of the normal to it at (1, 3/2) is

1. 2y - x = 2
2. 4x - 2y = 1
3. 4x + 2y = 7
4. x + 2y = 4

Solution

Eccentricity = 1/2

Let 2a be the length of major axis and 2b be the length of minor axis

a/e = 4

a = 2

Also, b = √3, as e = 1/2

Equation of ellipse is x²/4 + y²/3 = 1

Equation of normal at (1, 3/2) is 4x - 2y = 1

The correct option is B.