Obtain the differential equation of the family of circles passing through (a,0) and (-a,0) - Maths - Differential Equations

Question

Obtain the differential equation of the family of circles passing
through (a,0) and (-a,0)

Rahul Raj · Accepted Answer

Dear student

(a,0) and (-a,0)midpoint is (0,0)The center of these circles necessarily lie on the y axis, the perpendicular bisector of chord passes through centre This implies that their center can be represented as (h,k) where h=0  By Pythagoras theorem, the radius of such circle can be given by r =a2+k2  Now just substitute these values in the standard equation:  x2 + (y-k)2= a2+k2differentiating we get2x+2(y-k)dydx=0dydx=-xy-k

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Obtain the differential equation of the family of circles passing through (a,0) and (-a,0).