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The differential equations of the family of circles touching Y-axis at the origin is


Samadhan Ghule 25th Apr, 2018
Answer (1)
subhanshus s 10th May, 2018

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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