For Exercises 5-8, the given equation represents a conic section (nondegenerative case). Identify the type of conic section. (See Example 1) a. − 5 x 2 + 8 y + 4 = 0 b. 3 x 2 + 3 y 2 − 4 x + 2 y − 8 = 0 c. − 2 x 2 + y 2 − 4 y + 1 = 0
For Exercises 5-8, the given equation represents a conic section (nondegenerative case). Identify the type of conic section. (See Example 1) a. − 5 x 2 + 8 y + 4 = 0 b. 3 x 2 + 3 y 2 − 4 x + 2 y − 8 = 0 c. − 2 x 2 + y 2 − 4 y + 1 = 0
Solution Summary: The author explains the type of conic sections for the nondegenerate equations.
For Exercises 5-8, the given equation represents a conic section (nondegenerative case). Identify the type of conic section. (See Example 1)
a.
−
5
x
2
+
8
y
+
4
=
0
b.
3
x
2
+
3
y
2
−
4
x
+
2
y
−
8
=
0
c.
−
2
x
2
+
y
2
−
4
y
+
1
=
0
Curve that is obtained by the intersection of the surface of a cone with a plane. The three types of conic sections are parabolas, ellipses, and hyperbolas. The main features of conic sections are focus, eccentricity, and directrix. The other parameters are principal axis, linear eccentricity, latus rectum, focal parameter, and major and minor axis.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
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