Question on Differential Equations of a Family of Circles Q. The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is?



My Attempt:
I can write the equation of a random circle, satisfying the condition mentioned in the question, as:
$$(x – h)^2 + (y – 2)^2 = 25$$     

Differentiating, with respect to x,

$$2(x – h) + 2(y – 2) \frac{dy}{dx}= 0$$

I am not sure how to proceed further.
Can you eliminate the arbitrary constant $h$ from your system of equations? That will give you the answer.
Rearrange your equation:

$$2(y-2)\frac {dy}{dx}=-2(x-h)$$

$$\frac {dy}{dx}=-\frac{(x-h)}{(y-2)}$$