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# Conic Sections- Circle, Parabola, Ellipse, Hyperbola

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Conic Sections- Circle, Parabola, Ellipse, Hyperbola all topics covered. this is a presentation with excelent animations and explatition.

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### Conic Sections- Circle, Parabola, Ellipse, Hyperbola

1. 1. CONIC SECTIONS XI C
2. 2. α β THE INTERSECTION OF A PLANE WITH A CONE, THE SECTION SO OBTAINED IS CALLED A CONIC SECTION V m Lower nappe Upper nappe Axis Generator l This is a conic section.
3. 3. TYPES OF CONIC SECTIONS
4. 4. CIRCLE A CIRCLE IS THE SET OF ALL POINTS ON A PLANE THAT ARE EQUIDISTANT FROM A FIXED POINT ON A PLANE. O P(x,y)
5. 5. (h,k) C P(x,y) O (0,0) x² + y² = r² (x – h) ² + (y – k) ² = r² α β When β = 90°, the section is a circle Standard Equation General Equation
6. 6. TYPES OF CONIC SECTIONS
7. 7. ELLIPSE AN ELLIPSE IS THE SET OF ALL THE POINTS ON A PLANE, WHOSE SUM OF DISTANCES FROM TWO FIXED TWO REMAINS CONSTANT. P P P F F ¹ ³² ²¹
8. 8. α β O (0,c) (0,-c) (-b,0) (b,0) (0,-a) (0,a) x² y² a² b² — —+ = 1—+ x² y² b² a² — = 1 (-c ,0) (c, 0) When α < β < 90°, the section is an ellipse Vertical Ellipse Horizontal Ellipse (0,-b) (0,b) (a,0)(-a,0)
9. 9. .
10. 10. TYPES OF CONIC SECTIONS
11. 11. A PARABOLA IS THE SET OF ALL POINTS IN A PLANE THAT ARE EQUIDISTANT FROM A FIXED POINT A B V PARABOLA (VERTEX) F ( focus) 1 2 3 4O P 1 P2
12. 12. α β F(a,0)O x=-a y² = 4ax X' X Y' Y F(-a,0) O x=+a y² = -4ax X' X Y' Y F(0,-a) O y = a x² = 4ay X' X Y' Y F(0,a) O y = -a x² = -4ay X' X Y' Y When α = β, the section is an parabola Horizontal Parabola Horizontal Parabola Vertical Parabola Vertical Parabola
13. 13. TYPES OF CONIC SECTIONS
14. 14. HYPERBOLA F ( focus)V (verte x) A B A HYPERBOLA IS THE SET OF ALL POINTS,THE DIFFERENCE OF WHOSE DISTANCES FROM TWO FIXED POINTS IS CONSTANT V (verte x) F ( focus)
15. 15. α β Transverse axis F Conjugate axis F(c ,0)(a ,0)( -c ,0) (-a ,0) O F F(0 ,c) (0 ,a) (0 ,-c) (0 ,-a) O ¹ ¹ ² ² x² y² a² b² — —- = 1 - y² x² a² b² — —- = 1 When 0 ≤ β < α; the plane cuts through both the nappes & the curves of intersection is a hyperbola
16. 16. HYPERBOLIC PARABOLOIDSUNDIAL THERMAL POWER PLANT
17. 17. Conic Section Standard Eq. General Eq. Circle x² + y² = r² (x – h) ² + (y – k) ² = r² Parabola y² = 4ax (y-k)² = 4a(x+h) Ellipse Hyperbola x² y² a² b² — —+ = 1 (x-h)² (y-k)² a² b² — + — = 1 x² y² a² b² — —- = 1 (x-h)² (y-k)² a² b² — - — = 1