What is the vertex and radius of (x-3)^2 +(x-5)^2=100

Vertex is at and radius is .

Lets try to grasp on those numbers.

We know that the distance between two different points on a two-dimensional plane is defined by this formula,

.

Now imagine a circle with its vertex at point and a point lying on the circumference of this circle .

If we want to know the distance between these two points (radius) we use the general formula,

Squaring both sides gives us,

.

So what we are given the corresponding form to your equation.

In your case .

And which construct the vertex .

Hope this helps.