Answer:

Step-by-step explanation:
Apply exponent rule: 

Answer:
The center of the circle is at;

The radius of the circle is;

Explanation:
Given the equation of circle;

we want to re-write it in the form;

where;

Applying Completing the square method;

comparing the derived equation to the general form we have;

Therefore;
The center of the circle is at;

The radius of the circle is;
Answer:

Step-by-step explanation:
If the polynomial has one root as 1 + i, it's conjugate 1 - i will also be its root.
Therefore, the polynomial has roots 1 + i, 1 - i, and 3.
So, the polynomial function of lowest degree with rational coefficients will be
f (x) = (x - 3)(x - 1 - i)(x - 1 + i)
⇒
⇒
⇒
(Answer)
and
are the <em>farthest</em> from the origin and
is the <em>closest</em> from the origin.
Let be a curve of the form
. The distance with respect to origin is found by using the following Pythagorean identity:
(1)
Where
is the square distance function.
We can modify (1) as following:
![r = [27-3\cdot (y-2)^{2}]+y^{2}](https://tex.z-dn.net/?f=r%20%3D%20%5B27-3%5Ccdot%20%28y-2%29%5E%7B2%7D%5D%2By%5E%7B2%7D)


(1b)
Now we apply the First and second derivative tests to determine the minimum and maximum distances from the origin:
First derivative test


Second derivative test

The y-component represents a maximum.
Now we graph the function with the ressource of a graphing tool, we find the following points:
Farthest points:
,
.
Closest points:
.
and
are the <em>farthest</em> from the origin and
is the <em>closest</em> from the origin.
To learn more on ellipses, we kindly invite to check this verified question: brainly.com/question/19507943