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The equation of the normal to the parabo...

The equation of the normal to the parabola, `x^(2)=8y " at " x=4 ` is

A

`x+y=6`

B

`x+2y=0`

C

`3-2y=0`

D

`x+y=2`

Text Solution

Verified by Experts

The correct Answer is:
A
Putting `x=4 " in " x^(2)=8y, " we get " y=2. ` Now,
` rArr x^(2)=8y rArr2x=8(dy)/(dx) rArr (dy)/(dx)=(x)/(4) `
`rArr ((dy)/(dx))_((4","2))=1 `
The equation of the normal at (4,2) is
`y-2=-(1)/(1)(x-4) " or, " x+y=6 `
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