Find the distance between the centers of the circles x²+y²-2x+4y-11=0 and x²+y²+4x+2y-9=0.

Step-by-step explanation:

The standard form of a circle is

          .... (1)

where, (h,k) is center of the circle and r is radius.

If a expression is , then we need to add to make it perfect square.

The equation of first circle is

Add 5 on both sides.

        .... (2)

On comparing (1) and (2) we get

The center of first circle is (1,-2).

The equation of second circle is

Add 5 on both sides.

        .... (3)

On comparing (1) and (3) we get

The center of first circle is (-2,-1).

Distance formula:

The distance between the centers of the circles

Therefore, the distance between the centers of the circles is .

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