The eccentricity of an ellipse whose centre is at the origin is `1/2dot` if one of its directrices is `x=-4,` then the equation of the normal to it at `(1,3/2)` is: (1)`4x+2y=7` (2) `x+2y=4` (3) `2y-x=2` (4) `4x-2y=1`

Explanation

To find the equation of the normal to the ellipse at the point (1, 3/2), we will follow these steps:

### Step 1: Determine the parameters of the ellipse
Given the eccentricity \( e = \frac{1}{2} \) and one of the directrices \( x = -4 \), we can find \( a \) (the semi-major axis) using the relationship between the directrix and the eccentricity:
\[ -\frac{a}{e} = -4 \implies \frac{a}{\frac{1}{2}} = 4 \implies a = 4 \cdot \frac{1}{2} = 2. \]

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