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The eccentricity of an ellipse whose cen...

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

A

`x+2y=4`

B

`2y-x=0`

C

`4x-2y=1`

D

`4x+2y=7`

Text Solution

Verified by Experts

The correct Answer is:
B
Given eccentricity `,e=1//2`
Also, from the given equation of the directrrix,
`-(a)/(e)=-4rArra=2`
Now, `b^(2) =a^(2)(1-e^(2))=4(1-(1)/(4))=3`
So, equation of ellipse is `(x^(2))/(4)+(y^(2))/(3)=1`
Differentiating w.r.t.x., we get
`(dy)/(dx)=-(3x)/(4y)`
`:. ((dy)/(dx))_((1,3//2)) =-(3)/(4)xx(2)/(3)=-(1)/(2)`
`:.` Slope of the rormal =2 is `y-(3)/(2)=2(x-1) or 4x-2y=1`
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