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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:

A

`2y-x=2`

B

`4x-2y=1`

C

`4x+2y=7`

D

`x+2y=4`

Text Solution

Verified by Experts

The correct Answer is:
B
we have `e=(1)/(2) and (a)/( e )=4`
`therefore a=2`
Now,`b^(2)=a^(2)(1-e^(2))=(2)^(2)[1-((1)/(2))^(2)] =4(1-(1)/(4) )=3`
` implies b= sqrt(3)`
`therefore ` Equation of the normal at `( 1,(3)/(2))` is
`(a^(2)x)/(x_(1))-(b^(2)y)/(y_(1))= a^(2)- b^(2)`
`implies (4x)/(1)- (3y)/((3//2))=4-3`
`implies 4x- 2y=1`
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