Question

Consider the family of all circles having their center at the point (1,2). Write the equation of the family. Write corresponding differential equation

Answer 1

Let radius of circle is r. then, equation of circle is given by (x - 1)² + (y - 2)² = r²

hence, equation of circle is (x - 1)² + (y - 2)² = r².


now, differentiate equation of circle with respect to x,

2(x - 1) + 2(y - 1)dy/dx = 0

or, (x -1) + (y - 1)dy/dx = 0

or, x -1 + ydy/dx -dy/dx = 0

or, ydy/dx - dy/dx + x - 1 = 0 , it is the differential equation of family of circle.