Question

How do you write the equation of the circle with end points of the circle are (-3, 5) (9, -7)?

Answer 1

`(x-3)^2+(y+1)^2=72`

Explanation:

`"the standard form of the equation of a circle is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))`
where ( a , b ) are the coordinates of the centre and r the radius.

`"the centre of the circle is at the midpoint of the 2 given"`
`"points and the radius is the distance from the centre to"`
`"either of the 2 points"`

`"midpoint "=[1/2(-3+9),1/2(5-7)]=(3,-1)`

`"calculate distance between "(3,-1)" and "(-3,5)`

`"using the "color(blue)"distance formula"`

`r=sqrt((-3-3)^2+(5+1)^2)=sqrt72`

`"using " (a,b)=(3,-1)" and "r=sqrt72`

`rArr(x-3)^2+(y+1)^2=72" is the equation"`