Solutions for Rotation of Axes
Solutions to Try Its
1.- hyperbola
- ellipse
- hyperbola
- ellipse
Solutions to Odd-Numbered Exercises
1. The [latex]xy[/latex] term causes a rotation of the graph to occur. 3. The conic section is a hyperbola. 5. It gives the angle of rotation of the axes in order to eliminate the [latex]xy[/latex] term. 7. [latex]AB=0[/latex], parabola 9. [latex]AB=-4<0[/latex], hyperbola 11. [latex]AB=6>0[/latex], ellipse 13. [latex]{B}^{2}-4AC=0[/latex], parabola 15. [latex]{B}^{2}-4AC=0[/latex], parabola 17. [latex]{B}^{2}-4AC=-96<0[/latex], ellipse 19. [latex]7{{x}^{\prime }}^{2}+9{{y}^{\prime }}^{2}-4=0[/latex] 21. [latex]3{{x}^{\prime }}^{2}+2{x}^{\prime }{y}^{\prime }-5{{y}^{\prime }}^{2}+1=0[/latex] 23. [latex]\theta ={60}^{\circ },11{{x}^{\prime }}^{2}-{{y}^{\prime }}^{2}+\sqrt{3}{x}^{\prime }+{y}^{\prime }-4=0[/latex] 25. [latex]\theta ={150}^{\circ },21{{x}^{\prime }}^{2}+9{{y}^{\prime }}^{2}+4{x}^{\prime }-4\sqrt{3}{y}^{\prime }-6=0[/latex] 27. [latex]\theta \approx {36.9}^{\circ },125{{x}^{\prime }}^{2}+6{x}^{\prime }-42{y}^{\prime }+10=0[/latex] 29. [latex]\theta ={45}^{\circ },3{{x}^{\prime }}^{2}-{{y}^{\prime }}^{2}-\sqrt{2}{x}^{\prime }+\sqrt{2}{y}^{\prime }+1=0[/latex] 31. [latex]\frac{\sqrt{2}}{2}\left({x}^{\prime }+{y}^{\prime }\right)=\frac{1}{2}{\left({x}^{\prime }-{y}^{\prime }\right)}^{2}[/latex]
33. [latex]\frac{{\left({x}^{\prime }-{y}^{\prime }\right)}^{2}}{8}+\frac{{\left({x}^{\prime }+{y}^{\prime }\right)}^{2}}{2}=1[/latex]
35. [latex]\frac{{\left({x}^{\prime }+{y}^{\prime }\right)}^{2}}{2}-\frac{{\left({x}^{\prime }-{y}^{\prime }\right)}^{2}}{2}=1[/latex]
37. [latex]\frac{\sqrt{3}}{2}{x}^{\prime }-\frac{1}{2}{y}^{\prime }={\left(\frac{1}{2}{x}^{\prime }+\frac{\sqrt{3}}{2}{y}^{\prime }-1\right)}^{2}[/latex]
39.
41.
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51. [latex]\theta ={45}^{\circ }[/latex]
53. [latex]\theta ={60}^{\circ }[/latex]
55. [latex]\theta \approx {36.9}^{\circ }[/latex]
57. [latex]-4\sqrt{6}<k<4\sqrt{6}[/latex]
59. [latex]k=2[/latex]Licenses & Attributions
CC licensed content, Specific attribution
- Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution.
