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Find the equation of the tangent to the circle `x^2+y^2+4x-4y+4=0` which makes equal intercepts on the positive coordinates axes.

A

`x+ y =2`

B

` x + y = 2 sqrt( 2)`

C

` x +y = 4`

D

` x + y =8 `

Text Solution

Verified by Experts

Let the equations of the required tangent be `x + y = a,` then length of the perpendicular from centre = radius
`:. | ( -2+ 2-a)/(sqrt(2))|= 2 rArr a =2 sqrt(2), ( Q, a gt 0 ) ` .Hence, the equation of tangent is `x + y = 2 sqrt( 2) `.
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