Consider the equation: a₁x₁ + a₂x₂ = ao, where x₁ and x₂ are variables and ao, a₁, az are nonzero constants. No matter what the constants are, the graph of this equation will always be a line. Similarly, the graph of the equation: a₁x² + a₂x² = a₁ is always a conic section (ellipse or a hyperbola) with center (0,0). Furthermore, the axes of the conic section lie along the axes of the (x₁, x₂) plane. Give the general shapes of the graphs of the following equations, assuming all constants are nonzero: Specify (i) the general shape of the graph, (ii) the general location of the center (i.e.whether the center is (0,0), or on one of the axes, or
Consider the equation: a₁x₁ + a₂x₂ = ao, where x₁ and x₂ are variables and ao, a₁, az are nonzero constants. No matter what the constants are, the graph of this equation will always be a line. Similarly, the graph of the equation: a₁x² + a₂x² = a₁ is always a conic section (ellipse or a hyperbola) with center (0,0). Furthermore, the axes of the conic section lie along the axes of the (x₁, x₂) plane. Give the general shapes of the graphs of the following equations, assuming all constants are nonzero: Specify (i) the general shape of the graph, (ii) the general location of the center (i.e.whether the center is (0,0), or on one of the axes, or
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please do all part and please explain
Transcribed Image Text:Consider the equation: a₁x₁ + a₂x₂ = ao, where x₁ and x₂ are variables and ao, a₁, a₂
are nonzero constants. No matter what the constants are, the graph of this equation
will always be a line.
a
Similarly, the graph of the equation: α₁x² + ₂x² = α₁ is always a conic section
(ellipse or a hyperbola) with center (0,0). Furthermore, the axes of the conic section
lie along the axes of the (x₁, x₂) plane.
Give the general shapes of the graphs of the following equations, assuming all
constants are nonzero: Specify (i) the general shape of the graph, (ii) the general
location of the center (i.e.whether the center is (0,0), or on one of the axes, or
whether the center can be anywhere in the plane), and (iii) the general orientation of
the shape (i.e. whether it is aligned along one axis or the other, or whether it is
rotated).
a. α₁x² = a₁
ao
b. a₁x² = a₁
C. a₁x1x₂ = ao
d. a₁x² + ₂x₁ = a
e. a₁x² + a₂x₂ = ao:
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