[PLATO] A circle is centered at the point (5, -4) and passes through the point (-3, 2). The equation of this circle is (x + (1.) )² + (y+ (2.) )² = (3.)

1. -5

2. 4

3. 10

Step-by-step explanation:

this equation is in vertex form. Points 1 and 2 are the coordinates of the center of the circle (5 is the x coordinate, -4 is the y coordinate). To find the center of the circle, take the values of the given (5, -4) coordinate, and switch their sign (5 becomes -5, -4 becomes 4).

to find part 3, you will need to plug in the values of the second coordinate (-3, 2).

If you need to find the radius of (3), find the square root of whatever answer you got.

1. (x-5)^2 + (y+4)^2 = ___

2. (-3-5)^2 + (2+4)^2 = ____

3. (-8)^2 + (6)^2 =___

4. 64+36 = 100

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(to find radius)

5.

the answer to 3 is 10

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(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3