Q. 105.0( 1 Vote )

Find the differential equation of all the circles which pass through the origin and whose centers lie on the x - axis.

Answer :

Any circle with centre at (h, k) and radius r is given by,

(x – h)2 + (y – k)2 = r2

Here centre is on x - axis, so k = 0

So, we have the equation of circle as, (x – h)2 + y2 = r2

Further it is given that circle passes through origin (0,0) therefore origin must satisfy equation of circle. So, we get,

0 + h2 = r2

So, the equation of circle is (x – h)2 + y2 = h2

x2 – 2hx + y2 = 0

x2 + y2 = 2hx

Now, differentiating it with respect to x we get,

Hence, the required differential equation is

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