Question

distance between 2 centres of circle

Answer 1

For any two points $A(x_1,y_1)$ and $B(x_2,y_2)$ representing the centers of two circles, the distance $d$ between them is given by

$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}.$$

For example, in the similar problem the centers are taken as

$$A(0,3) \quad \text{and} \quad B(4\sqrt{5},4).$$

Then, the distance is

$$d= \sqrt{(4\sqrt{5}-0)^2+(4-3)^2}=\sqrt{80+1}=\sqrt{81}=9.$$

Distance between the two centers is $9$.

Answer 2

• Use the distance formula $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
• For centers $A(0,3)$ and $B(4\sqrt{5},4)$, calculate: $$d=\sqrt{(4\sqrt{5})^2+(1)^2}=\sqrt{80+1}=\sqrt{81}=9.$$