For Exercises 23-28, a. Determine an acute angle of rotation to eliminate the x y -term . (See Example 4) b. Use a rotation of axes to eliminate the x y -term to write the equation in the form A ' x ' 2 + C ' y ' 2 + D ' x ' + E ' y ' + F ' = 0 . c. Identify the type of curve represented by the equation. d. Write the equation in standard form and sketch the graph. x 2 − 2 3 x y + 3 y 2 − 16 3 − 16 y = 0
For Exercises 23-28, a. Determine an acute angle of rotation to eliminate the x y -term . (See Example 4) b. Use a rotation of axes to eliminate the x y -term to write the equation in the form A ' x ' 2 + C ' y ' 2 + D ' x ' + E ' y ' + F ' = 0 . c. Identify the type of curve represented by the equation. d. Write the equation in standard form and sketch the graph. x 2 − 2 3 x y + 3 y 2 − 16 3 − 16 y = 0
2.
Determine two different equations (one sine and one cosine)
that represent the curve. Explain your thinking with added
(-45, 1)
annotations.
-75
75
(15, -7)
a. At what point should the origin be shifted if the coordinates of a point (4, 5) become (-3, 9)?
b.The equation of a curve referred to the new axes, axes retaining their directions, and origin (4, 5) is X^2 + Y^2 = 36. Find the equation referred to the original axes.
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