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Study Guides > College Algebra

Solutions

Solutions to Try Its

1.
  • hyperbola
  • ellipse
2. x24+y21=1\frac{{{x}^{\prime }}^{2}}{4}+\frac{{{y}^{\prime }}^{2}}{1}=1 3.
  • hyperbola
  • ellipse

Solutions to Odd-Numbered Exercises

1. The xyxy 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 xyxy term. 7. AB=0AB=0, parabola 9. AB=4<0AB=-4<0, hyperbola 11. AB=6>0AB=6>0, ellipse 13. B24AC=0{B}^{2}-4AC=0, parabola 15. B24AC=0{B}^{2}-4AC=0, parabola 17. B24AC=96<0{B}^{2}-4AC=-96<0, ellipse 19. 7x2+9y24=07{{x}^{\prime }}^{2}+9{{y}^{\prime }}^{2}-4=0 21. 3x2+2xy5y2+1=03{{x}^{\prime }}^{2}+2{x}^{\prime }{y}^{\prime }-5{{y}^{\prime }}^{2}+1=0 23. θ=60,11x2y2+3x+y4=0\theta ={60}^{\circ },11{{x}^{\prime }}^{2}-{{y}^{\prime }}^{2}+\sqrt{3}{x}^{\prime }+{y}^{\prime }-4=0 25. θ=150,21x2+9y2+4x43y6=0\theta ={150}^{\circ },21{{x}^{\prime }}^{2}+9{{y}^{\prime }}^{2}+4{x}^{\prime }-4\sqrt{3}{y}^{\prime }-6=0 27. θ36.9,125x2+6x42y+10=0\theta \approx {36.9}^{\circ },125{{x}^{\prime }}^{2}+6{x}^{\prime }-42{y}^{\prime }+10=0 29. θ=45,3x2y22x+2y+1=0\theta ={45}^{\circ },3{{x}^{\prime }}^{2}-{{y}^{\prime }}^{2}-\sqrt{2}{x}^{\prime }+\sqrt{2}{y}^{\prime }+1=0 31. 22(x+y)=12(xy)2\frac{\sqrt{2}}{2}\left({x}^{\prime }+{y}^{\prime }\right)=\frac{1}{2}{\left({x}^{\prime }-{y}^{\prime }\right)}^{2} 33. (xy)28+(x+y)22=1\frac{{\left({x}^{\prime }-{y}^{\prime }\right)}^{2}}{8}+\frac{{\left({x}^{\prime }+{y}^{\prime }\right)}^{2}}{2}=1 35. (x+y)22(xy)22=1\frac{{\left({x}^{\prime }+{y}^{\prime }\right)}^{2}}{2}-\frac{{\left({x}^{\prime }-{y}^{\prime }\right)}^{2}}{2}=1 37. 32x12y=(12x+32y1)2\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} 39. 41. 43. 45. 47. 49. 51. θ=45\theta ={45}^{\circ } 53. θ=60\theta ={60}^{\circ } 55. θ36.9\theta \approx {36.9}^{\circ } 57. 46<k<46-4\sqrt{6}<k<4\sqrt{6} 59. k=2k=2

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  • Precalculus. Provided by: OpenStax Authored by: OpenStax College. Located at: https://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution.