If the coordinates of the endpoints of a diameter of the circle are known, the equation of a circle can be found. first, find the midpoint of the diameter, which is the center of the circle. then find the radius, which is the distance from the center to either endpoint of the diameter. finally use the center-radius form to find the equation. find the center-radius form for the circle having the endpoints left parenthesis 5 comma 2 right parenthesis and left parenthesis negative 7 comma 4 right parenthesis of a diameter.

Given

Endpoints of the diameter (5,2) and (-7,4)

Step One

Find the center

Center = (x2 + x1)/2 , (y2 + y1)/2

x2 = -7; x1 = 5; y2 = 4; y1 = 2

Center = (-7 + 5)/2 ; (4 + 2)/2;

Center = (-1 , 3)

Step Two

Find the radius squared using the distance formula. Use (5,2) as the second point. The other point is the center.

Distance squared = (5 - - 1)^2 + (2 - 3)^2

Distance squared = ( 6)^2 + (-1 )^2

Distance squared = 37

Step Three

State the circle's formula

(x - - 1 )^2 + (y - 3)^2 = 37

(x + 1)^2 + (y - 3)^2 = 37

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

you have orange juice on wednesday. (idk why this is the answer)

step-by-step explanation: