[The graphs are labeled (a), (b), (c), (d), (e), and (f).] (a) (b) -5-4-3-2–1-- (c) (d) (e) (f) 1. + y = 25 2. 4x + 4y? = 25 %3D 3. (r-2)2 + (y – 3)² = 9 4. (x+ 1)2 + (y – 3)² = 9
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
![3. Which standard form of the equation of a par
Explain ow you
radius of the circle given by the equation
x+ y - 36 = 0:
entir
the center and
would you use to write an equation for parab
with vertex (2,-3) and focus (2, 1) Explain your
reasoning.
2. Is the center of the circle given by the equation
(x + 2)2 + (y + 4)2 = 20 shifted two units to the
right and four units upward? Explain your reasoning.
4. Given the equation of a parabola, explain how to
determine if the parabola opens upward, dowaward,
to the right, or to the left.
12.1 EXERCISES
Go to pages 804-805 to
record your assignments.
Developing Skills.
In Exercises 1-6, match the equation with its graph.
[The graphs are labeled (a), (b), (c), (d), (e), and (f).]
5. y = -4 -ř
6. y = 4 -
(a)
(b)
In Exercises 7-14, write the standard form of the
equation of the circle with center at (0, 0) that satisfies
the criterion. See Example 1.
7. Radius: 5
8. Radius: 9
9. Radius:
10. Radius:
(c)
(d)
11. Passes through the point (0, 6)
12. Passes through the point (-2, 0)
13. Passes through the point (5, 2)
14. Passes through the point (-1, -4)
In Exercises 15–22, write the standard form of the
equation of the circle with center at (h, k) that satisfies
the criteria. See Example 3.
(e)
(f)
O 15. Center: (4, 3)
Radius: 10
16. Center: (-4, 8)
Radius: 7
1. + y 25
2. 4x + 4y2 = 25
3. (x-2)2 + (y – 3)2 = 9
4. (x+ 1)2 + (y – 3)² = 9
17. Center: (6, -5)
Radius: 3
70
Chapter 12
Conics
8. Center: (-5,-2)
In Exercises 43-46, use a graphing calculator to graph](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f20e3e5-fc79-4867-ba6f-7d4cd7ce329b%2F76338595-1b47-45a4-89f3-d904d3c54647%2Fwjij0dm_processed.jpeg&w=3840&q=75)
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