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To find: a sine and cosine angle and say whether the equation is an ellipse, hyperbola or parabola.
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Answer to Problem 30E
The new equation is a hyperbola.
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 is a hyperbola, having coefficients.
Conclusion:
The new equation is a hyperbola.
The angle is
Sine and cosine angle is,
Chapter A5 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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