The differential equation of family of circles with fixed radius 5 units and centre on the line $y=2$, is
Answer & explanation
Correct answer: option 1
Let $(a, 2)$ be the centre of the circle, where 'a' is a variable. Then, the equation of the family of circles is
$(x-a)^2+(y-2)^2=5^2$ ......(i)
Differentiating w.r. to $x$, we get
$2(x-a)+2(y-2) \frac{d y}{d x} \Rightarrow x-a=-(y-2) y_1$
Substituting this value of $(x-a)$ in (i), we get
$(y-2)^2 y_1^2=25-(y-2)^2$
as the required differential equation.