Fórmulas Geometria Analítica: Superfícies Quádricas

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Geometria Analítica: Superfícies Quádricas

1. Imaginary Elliptic Cylinder (Case 10)

\frac{x^2}{a^2}+\frac{y^2}{b^2}=-1

2. Legenda

3. Hyperbolic Cylinder (Case 11)

\frac{x^2}{a^2}-\frac{y^2}{b^2}=1

4. Equação quádrica (forma geral)

Ax^2+By^2+Cz^2+2Fyz+2Gzx+2Hxy+2Px+2Qy+2Rz+D=0

5. Real Intersecting Planes (Case 12)

\frac{x^2}{a^2}-\frac{y^2}{b^2}=0

6. Classificação das superfícies quádricas

(............TABELA.............) \\ Here\\ e= \begin{pmatrix} A & H & G \\ H & B & F \\ G & F & C \end{pmatrix} \\ E= \begin{pmatrix} A & H & G & P \\ H & B & F & Q \\ G & F & C & R \\ P & Q & R & D \end{pmatrix} \\ \Delta=det(E) \\ k_{1},k_{2},k_{3} are the roots of the equation. \\ \begin{vmatrix} A-x & H & G \\ H & B-x & F \\ G & F & C-x \end{vmatrix} =0

7. Imaginary Intersecting Planes (Case 13)

\frac{x^2}{a^2}+\frac{y^2}{b^2}=0

8. Real ellipsoid (Case 1)

\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1

9. Parabolic Cylinder (Case 14)

\frac{x^2}{a^2}-y=0

10. Hyperboloid of 1 Sheet (Case 3)

\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1

11. Real Parallel Planes (Case 15)

\frac{x^2}{a^2}=1

12. Hyperboloid of 2 Sheets (Case 4)

\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=-1

13. Real quadric cone (Case 5)

\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=0

14. Imaginary Parallel Planes (Case 16)

\frac{x^2}{a^2}=-1

15. Imaginary Quadric cone (Case 6)

\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=0

16. Coincident Planes (Case 17)

x^2=0

17. Elliptic paraboloid (Case 7)

\frac{x^2}{a^2}+\frac{y^2}{b^2}-z=0

18. Imaginary Ellipsoid (Case 2)

\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=-1

19. Hyperbolic Paraboloid (Case 8)

\frac{x^2}{a^2}-\frac{y^2}{b^2}-z=0

20. Real elliptic cylinder (Case 9)

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1