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Math Help - help please

  1. #1
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    help please

    Find the equation of the circle with diameter AB where A is (4, 7) and B is (2, 3)
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  2. #2
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    S=(\frac{x_A+x_B}{2};\frac{y_A+y_B}{2})=(\frac{4-2}{2};\frac{7+3}{2})=(1,5)
    r=\frac{|AB|}{2}=\frac{\sqrt{6^2+4^2}}{2}=\frac{\s  qrt{52}}{2}
    (x-1)^2+(y-5)^2=r^2
    (x-1)^2+(y-5)^2=\frac{13}{2}
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Arch_Stanton View Post
    S=(\frac{x_A+x_B}{2};\frac{y_A+y_B}{2})=(\frac{4-2}{2};\frac{7+3}{2})=(1,5)
    r=\frac{|AB|}{2}=\frac{\sqrt{6^2+4^2}}{2}=\frac{\s  qrt{52}}{2}
    (x-1)^2+(y-5)^2=r^2
    (x-1)^2+(y-5)^2=\frac{13}{2}
    You need to provide some words describing what you are doing and why.

    CB
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  4. #4
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    Quote Originally Posted by CaptainBlack View Post
    You need to provide some words describing what you are doing and why.

    CB
    Quote Originally Posted by Arch_Stanton View Post

    1. S=(\frac{x_A+x_B}{2};\frac{y_A+y_B}{2})=(\frac{4-2}{2};\frac{7+3}{2})=(1,5)
    2. r=\frac{|AB|}{2}=\frac{\sqrt{6^2+4^2}}{2}=\frac{\s  qrt{52}}{2}
    3. (x-1)^2+(y-5)^2=r^2
    4. (x-1)^2+(y-5)^2=\frac{13}{2}
    I took the liberty and wrote an explanation. I hope no one has any objections.

    Before starting, I want to point out a mistake in 4. We have found the radius to be \frac{\sqrt{52}}{2} = \frac{\not{2}\sqrt{13}}{\not{2}}. Therefore, r^2 is 13 and not 13/2.

    To find the equation of the circle with the given information, we need two things: the magnitude of the radius and the coordinate of the center. Recall that the equation of the circle is of the form:
    (x-h)^2+(y-k)^2 = r^2

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

    1. Taking the average of the individual x and y coordinates yields the midpoint of diameter AB, which is also the center of the circle.

    2. Using the distance formula:
    d^2 = (x_2 - x_1)^2 + (y_2-y_1)^2

    we find the measure of the diameter AB. Dividing it by 2 yields the radius.

    3 & 4. Replacing in the equation of the circle yields:
    (x-1)^2+(y-5)^2 = 13
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