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.

Answer

`x+y=+-2sqrt(2)`

Explanation

Let the equation of the tangent be
`(x)/(a)+(y)/(a)=1`
i.e., `x+y=a ` (1)
Therefore, the length of perpendicular from the center (-2,2) on (1) is equal to the radius, i.e., `sqrt(4+4-4)` . So,
`(|-2+2-a|)/(sqrt(1+1))=2`
or `a= + 2 sqrt(2)`
Hence, the equations of the tangents are `x+y= +- 2 sqrt(2)`.