(a)
To describe: the representation of the equation.
(a)
Answer to Problem 44E
Here, the given equation represents a parabola.
Explanation of Solution
Given:
Calculation:
Given Equation:
To decide whether the given equation represents a parabola, an ellipse, or a hyperbola.
Comparing with the standard equation for a Quadratic Curve,
Thus,
Now, discriminate
Since
Conclusion:
Hence, the given equation represents a parabola.
(b)
To show: the graph of the equation is a given line.
(b)
Answer to Problem 44E
Here, the curve is a degenerate parabola which is a straight line.
Explanation of Solution
Given:
line
Calculation:
The left hand side of the given equation factors as a perfect square.
Therefore, the equation becomes
So, the curve is a degenerate parabola (i.e. a straight line).
Conclusion:
Therefore, the curve is a degenerate parabola which is a straight line.
Chapter A5 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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