Question

Que. 4. Find differential equation of the circle
passing through the origin and having its cen-
tre on the Y-axis.​

Answer 1

Answer:

Form the differential equation of all circles which pass through origin and whose centre lie on Y-axis.

(x−0)2+(y−k)2=k2.

x2+(y−k)2=k2.

x2+y2−2ky=0.

2yx2+y2=k .....(1)

4y22y(2x+2ydxy)−(x2+y2)dx2dy=0.

4y(x+ydxdy)−2(x2+y2)dxdy=0.

4xy=4y2dxdy−2(x2+y2)dxdy=0.

(4y2−2x2−2y2)dxdy+4xy=0.

Step-by-step explanation:

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