Question

How do you write the equation for a circle with the endpoints of a diameter at (4, -3) and (-2, 5)?

Answer 1

`(x-1)^2+(y-1)^2=25`

Explanation:

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

`"we require to find the centre and radius"`

`"given the endpoints of the diameter then the centre"`
`"is at the midpoint and the radius is the distance from"`
`"the centre to either of the endpoints"`

`"midpoint "=[1/2(4-2),1/2(5-3)]`

`rArr"centre "=(1,1)`

`"using "(1,1)" and "(4,-3)`

`r=sqrt((4-1)^2+(-3-1)^2)=sqrt(9+16)=5`

`(x-1)^2+(y-1)^2=25larrcolor(red)"equation of circle"`