Question

Find the distance between the centers of the circles (x-1)²+(y+2)²=16 and (x+2)²+(y+1)²=14.

Answer 1

Answer:$D=\sqrt{10}$

Step-by-step explanation:

Given

circle

$\left ( x-1\right )^2+\left ( y+2\right )^2=16$

center of circle is (1,-2)

second circle

$\left ( x+2\right )^2+\left ( y+1\right )^2=14$

center of circle is (-2,-1)

Distance between two points

$D=\sqrt{\left ( y_2-y_1\right )^2+\left ( x_2-x_1\right )^2}$

$D=\sqrt{\left ( -2+1\right )^2+\left ( 1+2\right )^2}$

$D=\sqrt{10}$