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If the line ax + y = c, touches both t...

If the line `ax + y = c`, touches both the curves `x^(2) + y^(2) =1 and y^(2) = 4 sqrt2x`, then `|c|` is equal to:

A

`(1)/(2)`

B

`sqrt2`

C

2

D

`(1)/(sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
`ax + y =c` is a tangent to
`x^(2) + y^(2) =1`…(1)
and `y^(2) = 4 sqrt2x`…(2)
equation of common tangent to (1) and (2)
`y = mx + (sqrt2)/(m)`
is also tangent to (1)
So `(|(sqrt2)/(m)|)/(sqrt(1+m^(2))) =1 rArr (2)/(m^(2)) = (1 + m^(2)) rArr m^(4) + m^(2) -2 = 0`
`(m^(2) + 2) (m^(2) -1) = 0, m = +-1`
Common tangent will be `y=x + sqrt2 and y = -x - sqrt2`
On comparing `a = -1, c = sqrt2 and a =1 and c = -sqrt2`
`|c| = sqrt2`
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