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  4. The equation of the tangent to the circle x2+y2+4x-4y+4=0 which make equal intercepts on the positive coordinate axes is:

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Q. The equation of the tangent to the circle $ {{x}^{2}}+{{y}^{2}}+4x-4y+4=0 $ which make equal intercepts on the positive coordinate axes is:

JamiaJamia 2005

Solution:

Let the equation of the required tangent be $ x+y=a $ then, length of the perpendicular from centre = radius $ \left| \frac{-2+2-a}{\sqrt{2}} \right|=2 $ $ \Rightarrow $ $ a=2\sqrt{2} $ Hence, the equation of tangent is $ x+y=2\sqrt{2} $