Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.

Explanation

The center of circle will be on line `x+y=0`. It will be in `2nd` quadrant. Circle touching both `x` and `y` axes

Centre will be `(-a, a)`

Radius = `a`



The equation of the family of circles will then be

`(x+a)^{2}+(y-a)^{2}=a^{2} \ \ \ ...(i)`


Differentiate w.r.t `x`

`therefore 2(x+a)+2(y-a) y'=0 `

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