Question

Find the center and radius of circle `(x-3)^3+(y+4)^2=10`?

Answer 1

Coordinates of the centre of the circle are `(3,-4)` and circle's radius is `sqrt10`.

Explanation:

Perhaps you mean the equation to be `(x-3)^2+(y+4)^2=10`

As `(x-3)^2+(y+4)^2=10` is equivalent to

`(x-3)^2+(y-(-4))^2=(sqrt10)^2`

or `sqrt((x-3)^2+(y-(-4))^2)=sqrt10`

The Left hand side shows that the distance of `(x,y)` from point `(3,-4)`

and as the equation indicates that this is always `sqrt10`

Equation `(x-3)^2+(y+4)^2=10` indicates that `(x,y)` is always at a distance of `sqrt10` from `(3,-4)`.

Hence, coordinates of the centre of the circle are `(3,-4)` and circle's radius is `sqrt10`.