Question

How do you write the equation for a circle centered at (h,k) = (5,-8) and passing through the point (3,-2)?

Answer 1

`(x-5)^2+(y+8)^2=40`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)((x-h)^2+(y-k)^2=r^2)color(white)(2/2)|)))`

`"where "(h,k)" are the coordinates of the centre and r"`
`"is the radius"`

`"the radius r is the distance from the centre to the point"`
`"on the circumference"`

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

`•color(white)(x)r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

`"let "(x_1,y_1)=(5,-8)" and "(x_2,y_2)=(3,-2)`

`r=sqrt((3-5)^2+(-2+8)^2)=sqrt(4+36)=sqrt40`

`(x-5)^2+(y+8)^2=40larrcolor(blue)"is equation of circle"`