Write the equation of the circle in general form. show all of your work

In this exercise we have the general form of the equation of a circle, which is given by:

The ordinary equation of a circle is:

But this can be written as:

From the original equation we know that:

Finally:

We need to write this equation in the form:

Since:

Then we need to find the center and radius in order to get D, E and F then. From the graph, it is easy to know that the center is and the radius is 2. Therefore:

Finally, the general form of the equation is:

A parabola is the set of all points in a plane that are equidistant from  a fixed line called the directrix and a fixed point called the focus that does not lie on the line. Since the directrix is then this is a horizontal axis. So the standard for of the equation of a parabola that matches this form is:

The vertex is so our goal is to find :

We can find the absolute value of as follows:

Since the directrix is to the left of the vertex, the parabola opens to the left and hence:

.

Finally, the equation is:

answer is more than one

step-by-step explanation: