Find the differential equation of all circles tangent to y-axis
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Find the differential equation of all circles tangent to y-axis
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Let the circle with centre (a, b) be tangent to the y-axis.
Then, the radius of the circle must be b.
Therefore the equation of the circle is
(x – a)2 + (y – b)2 = b2
or x2 – 2ax + a2 + y2 – 2by = 0
Then 2x – 2a + 2ydy/dx – 2bdy/dx = 0
ie x – a + ydy/dx – bdy/dx
(y – b)dy/dx = a – x
so dy/dx = (a – x)/(y – b) or -(x – a)/(y – b)