To find: a sine and cosine angle and say whether the equation is an ellipse, hyperbola or parabola.
Answer to Problem 32E
The new equation forms parallel horizontal lines.
The angle is
Sine and cosine angle is,
Explanation of Solution
Given:
Calculation:
Comparing with the standard equation for a quadratic curve,
Thus,
For the cross-product term to vanish, the coordinate axes must be rotated by an angle
Now, using calculator calculate the angle ,
And,
After rotation of coordinate axes, the original coordinates,
Substituting the above values of
Simplify
Hence, the new equation forms parallel horizontal lines, having coefficients.
Conclusion:
The new equation forms parallel horizontal lines.
The angle is
Sine and cosine angle is,
Chapter A5 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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