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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

`4 sqrt(3)`

B

`3 sqrt(2)`

C

`2 sqrt(2)`

D

`3 sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Applying condition of tangency for circle and parabola
`C = r sqrt(1 + m^(2))` and `C = (a)/(m)`, `4 = 2 sqrt(1 + m^(2))` and `2 = (a)/(m)`
`1 + m^(2) = 4 implies = +- sqrt(3) implies a = 4 sqrt(3)`
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