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

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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