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 .

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)