Q. 135.0( 1 Vote )

# Form the differential equation of the family of circles passing through the fixed point (a,0) and (-a,0), where a is the parameter.

Now, it is not necessary that the centre of the circle will lie on origin in this case. Hence let us assume the coordinates of the centre of the circle be (0, h). Here, h is an arbitrary constant.

Also, the radius as calculated by the Pythagoras theorem will be a2 + h2.

Hence, the equation of the family of circles passing through the fixed point (a,0) and (-a,0), where a is the parameter can be represented by

(x)2+(y – h)2= a2 + h2, where a is an arbitrary constants.

(1)

Differentiating the above equation with respect to x on both sides, we have,

Substituting the value of a in equation (1)

This is the required differential equation.

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