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If y=mx+6 is a tangent to both the para...

If y=mx+6 is a tangent to both the parabolas `y^2=8x` and `x^2=3by` , then b is equal to :

A

36

B

`-36`

C

72

D

`-72`

Text Solution

Verified by Experts

The correct Answer is:
D
`y = mx + a/m` is tangent to `y ^(2) =4 ax`
So, ` 6 = 2/m implies m = 1/3`
Now,` y = x/3+6` is tangent to `x ^(2) = 3by`
`implies x ^(2) = (3b )(x/(3)+ 6) `
`x ^(2) =bx + 18b`
`x ^(2) = bx + 18b`
`x ^(2) - bx -18b =0`
` D =0 b ^(2) = 4 xx ( -18) b ^(2) (b ne 0)`
`b =-72`
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