Question

Is the distance between the center of the ellipse and the center of the epicenter equal in both cases?​

Answer 1

Answer:

The definition of a circle is as simple as the shape. A circle is the set of all points that are at a certain distance from a center point. This definition is what gives us the concept of the radius of a circle, which is equal to that certain distance.

Since we know a circle is the set of points a fixed distance from a center point, let’s look at how we can construct a circle in a Cartesian coordinate plane with variables xx and yy. To find a formula for this, suppose that the center is the point (a,b)(a,b). According to the distance formula, the distance cc from the point (a,b)(a,b) to any other point (x,y)(x,y) is:

c=√(x−a)2+(y−b)2c=(x−a)2+(y−b)2

If we now square this equation on both sides, we have:

c2=(x−a)2+(y−b)2c2=(x−a)2+(y−b)2

Remember that the distance between the center (a,b)(a,b) and any point (x,y)(x,y) on the circle is that fixed distance, which is called the radius. So let’s change this equation so that it uses rr instead of cc.

r2=(x−a)2+(y−b)2r2=(x−a)2+(y−b)2

This is the general formula for a circle with center (a,b)(a,b) and radius rr. Notice that all we have done is slightly rearrange the distance formula equation.