Question

given two points A(2,-5) and B(-4,3), find the equation of the circle with diameter AB.

Answer 1

(x-x1) (x-x2) + (y-y1) (y-y2) = 0

Answer 2

where (x1,y1) => (2,5) and (x2,y2)==> (-4,3)

Answer 3

what the name if this formula ?

Answer 4

of*

Answer 5

https://en.wikipedia.org/wiki/Circle#Equations

Answer 6

do anyone know what happens to the diameter ?

Answer 7

(x-h)^2 - (y-k)^2 = r^2 is the formula of the circle. you were given the two points of the diameter. you have to get the point of the center of the circle and you replace its value to the values of h and k. the center is C (h, k) your h is the x value of your center and k is the y value of your center. since you were given the points of the diameter, you just have to get the distance from point to point to get its length. divide it by 2 to get the value of you radius which is r in the equation. substitute all values to the equation then solve to get the equation of the circle. :)

Answer 8

Find the Midpoint:
\[\large M_{AB}=(-1,-1)\]
Find the distance between the midpoint and one of the points given in the question. (either A or B).
\[\large d_{MA}=\sqrt{(2--1)^2+(-5--1)^2}\]
\[\large =\sqrt{9+16}\]
\[\large =5\]
Now the midpoint is your center. And the distance between the midpoint/center and the point A or B.
So your equation of a circle in general form is:
\[\large (x-h)^2+(y-k)^2=r^2\]
where:
the centre of the circle is (h, k)
and the radius is r.
Substituting your midpoint as your centre and the distance found as your radius you will get this:
\[\large (x+1)^2+(y+1)^2=25\]