a)
To find: The type of the
The graph of equation
Given information:
The equation is
Calculation:
Draw the graph of equation
Therefore, the graph represents a hyperbola.
b)
To find: The equation in terms of
The required equation in terms of
Given information:
The equation is
Formula used:
Formula used to find the rotation angle
Here, A , B , and C are the values obtain by comparing given equation with equation
The equations for the axis of rotation are,
Calculation:
Comparing the given equation with the general equation,
Calculate the angle of rotation.
Divide the obtained equation by 2 to obtain the value of
Substitute
Substituting the values of x and y in given equation.
The equation
c)
To find: The vertex or vertices of equation
The vertices of equation
Given information:
The equation is
The equation in
Formula used:
The standard formula for a hyperbola is,
Vertices of hyperbola are:
Calculation:
Comparing this equation with standard equation of hyperbola.
Therefore, the vertices of hyperbola are
d)
To find: The vertices of ellipse in
The vertices of equation
Given information:
The equation is
The equations for the rotation of axis are,
The vertices of equation
Calculation:
Write the equation of the rotation of axis in terms of x and y .
Substitute the values
Similarly,
Substitute the values
Similarly,
The vertices of equation
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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