The differential equations of the family of circles touching Y-axis at the origin is
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Hey there,
It is given that the circle touches the y-axis at origin
Hence the equation of the circle is (x−a)2+(y-0)2=(a)2
Step 1:
(x−a)2+(y)2=(a)2
On simplifying we get,
(x)2−2ax+(a)2+(y)2=(a)2
(x)2+y2=2ax------(1)
Step 2:
Differentiating on both sides we get,
2x+2yy′=2a
dividing throughout by 2 we get
x+yy′=a-----(2)
Step 3:
Substituting equ(2) in equ(1) we get
x2+y2=2(x+yy′)x
On simplifying and rearranging we get
x2+2xyy′=y2
This is the required equation.
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