Question

Find the equation with enfpoints

Answer 1

`\text{centre = (}(1)/(2)\text{ (-4 + 4), }(1)/(2)(1-5))\text{ = (}0,-2)\text{ }`

the radius is the distance from the centre to either of the 2 given points

Let (x1, y1) = (-4,1) and (x2,y2) = (4,-5) (the given points)

then:

`r\text{ = d = }\sqrt[]{(4-(-4))^2+(-5-1)^2}\text{ = }\sqrt[]{(8)^2+(-6)^2\text{ = }}\text{ 10}`

then, take the equation of the circle is:

`(x-0)^2+(y+2)^2\text{ = 10}`

that is:

`(x)^2+(y+2)^2\text{ = 10}`