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If the line y = mx + 4 is tangent to x^(...

If the line y = mx + 4 is tangent to `x^(2) + y^(2) = 4` and `y^(2) = 4ax` then a is (a `gt` 0) equal to :

A

`4sqrt3`

B

`3sqrt2`

C

`2sqrt2`

D

`3sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
A
Applying conditions of tangency for circle and parabola .
`C = r sqrt(1+m^(2)) and C = (a)/(m), " " 4 = 2sqrt(1+m^(2)) and 2 = (a)/(m)`
`1+m^(2) = 4 " " rArr m = pm sqrt(3) rArr " "a = 4sqrt(3)`
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