Mathematics.................
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<h2>1. What are the center and equation of the circle?</h2>
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: