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Mathematics 59 Online
OpenStudy (anonymous):

FIND THE EQUATION OF A CIRCLE,DIAMETER AB,WHERE A=(1,3) AND B=(3,7)

Directrix (directrix):

What is the length of segment AB where A=(1,3) AND B=(3,7)?

Directrix (directrix):

Did you get 2√5 for AB ? @lissafi

Directrix (directrix):

The standard form for the equation of a circle is: (x - h) ^2 + (y-k)^2 = r^2 where (h,k) is the center of the circle and the radius is r.

Directrix (directrix):

If the diameter is 2√5, then the radius is √5. Now, we need the center of the circle.

Directrix (directrix):

The center will be the midpoint of the diameter A=(1,3) AND B=(3,7).

Directrix (directrix):

The midpoint coordinates of a segment are the average of the x-coordinates and y-coordinates of the endpoints, in this case, of segment AB.

OpenStudy (anonymous):

the question just said: find the equetion of the circle satisfying the given condition.Diameter AB, where A=(1,3) AND B=(3,7)

Directrix (directrix):

Right. To find that equation, we have to know the radius of the circle.

Directrix (directrix):

Also, we have to know the center of the circle.

Directrix (directrix):

We need to know how far it is from A to B. I got 2√5. Did you check it to see if I got the right answer?

Directrix (directrix):

The midpoint of segment AB is (2,5) which means the point (2,5) is the center of the circle.

Directrix (directrix):

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