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The length of the chord of the parabola ...

The length of the chord of the parabola `x^(2) = 4y` having equations `x - sqrt(2) y + 4 sqrt(2) = 0` is

A

`8sqrt(2)`

B

`2sqrt(11)`

C

`6sqrt(3)`

D

`3sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
C

`x^(2)=4y .....(i)`
`x-sqrt(2)y+4sqrt(2)=0`
`x=sqrt(2)y-4sqrt(2).......(ii)`
For Point of intersection we will solve both the equation
`(sqrt(2)y-4sqrt(2))^(2)=4y`
`2y^(2)+32-16y=4y`
`y^(2)-10y+16=0`
`y^(2)-2y-8y+16=0`
`(y-2)(y-8)=0`
`y=2, y=8`
`x^(2)=8`
`x=pm 2sqrt(2)`
`A=-2sqrt(2),2)`
`x^(2)=32`
`x=pm 4sqrt(2)`
`B(4 sqrt(2),8)`
`"(dist)"_(AB)=sqrt((4sqrt(2)-(-2sqrt(2)))^(2)+(8-2)^(2))`
`=sqrt(36xx2+36)`
dist `=6sqrt(3)`
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