The equation of the common tangent touching the circle `(x-3)^2+y^2=9` and the parabola `y^2=4x` above the x-axis is `sqrt(3)y=3x+1` (b) `sqrt(3)y=-(x+3)` `sqrt(2)y=x+3` (d) `sqrt(3)y=-(3x-1)`

Options

A. `sqrt3y=3x+1`
B. `sqrt3y=-(x+1)`
C. `sqrt3y=(x+1)`
D. `sqrt3y=-(3x+1)`

Answer

C

Explanation

The equation of any tangent to `y^(2)=4ax` is
`y=mx+1/m`
It will touch the circle `(x-3)^(2)+y^(2)=9`, if
`|(3m-0+1/m)/(sqrt(1+m^(2)))|=3`
`rArr" "(3m^(2)+1)^(2)=9m^(2)(m^(2)+1)`
`rArr" "3m^(2)=1`
`rArr" "m=+-1/sqrt3rArrm=1/sqrt3" "[because"Tangent is above x-axis"]`
Hence, the required tangent is
`y=x/sqrt3+sqrt3" or, "sqrt3y=x+3`