Question

Write an equation in general form of the circle withthe given properties.Center at(-8,9)and passing through the origin

Answer 1

the general equation of the circle with center (h,k) and radius r is given by the following equation:

`(x-h)^2+(y-k)^2=r^2`

In this case, we have that:

(h,k) = (-8,9)

then, we have provisionally:

`(x+8)^2+(y-9)^2=r^2`

to complete this equation, we must find the radius of the circle. Note that the given circle passes through the origin, that is, the circle passes through the point (x,y)=(0,0), then, replacing these coordinates into the above equation, we get:

`(0+8)^2+(0-9)^2=r^2`

this is equivalent to:

`(8)^2+(-9)^2=r^2`

this is equivalent to:

`64+81=r^2`

this is equivalent to:

`r^2=145`

solving for r, we get:

`r=\sqrt[]{145}=\text{ 12.04}`

so that, we can conclude that the equation in the general form of the given circle would be:

`(x+8)^2+(y-9)^2=(12.04)^2`