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The eccentricity of an ellipse whose cen...

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: `4x+2y=7` (2) `x+2y=4` (3) `2y-x=2` (4) `4x-2y=1`

A

`4x+2y=7`

B

`x+2y=4`

C

`2y-x=2`

D

`4x-2y=1`

Text Solution

Verified by Experts

Eccentricity of the given ellipse`, e = 1/2`
Equation of the directrix,
`x = -4`.
`:. +- a/e = -4`
`=> +-a/(1/2) = -4`
`=> a = +-2`
`=>a^2 = 4`
Now, we know, `e^2 = 1- b^2/a^2`
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