Conic Section Formula

1. Equation of conic section.

Equation of conic section

Note :

(a). If e = 1 the conic is called parabola.

(b). If e < 1 the conic is called ellipse.

(c). If e > 1 the conic is called hyperbola.

(d). If e = 0 the conic is called circle.

(e). If c = ∞ the conic is called pair of straight lines.

2. Standard equation of parabola.

Standard equation of parabola

3. Standard equation of an ellipse.

Standard equation of an ellipse

4. Standard equation of an hyperbola.

Standard equation of an hyperbola

5. Parametric equation of conic section.

6. General equation of the second degree.

General equation of the second degree

7. The general equation of the second degree.

The general equation of the second degree

8. Notations of conic Section.

Notations of conic Section

9. Equation of the tangent at any point (x1 , y1 ).

Equation of the tangent at any point (x1 , y1 )

10. Equation of the tangent at point.

Equation of the tangent at point.

11. The condition of tangency of y = mx + c to

The condition of tangency of y = mx + c to

12. The equation of normal to the parabola , ellipse and hyperbola.

The equation of normal to the parabola , ellipse and hyperbola

13. The equation of the chord of contact of tangents from (x1, y1) to the conic S = 0 is T = 0

14. The equation of the chord of contact of tangents from (x1, y1) to the

The equation of the chord of contact of tangents from (x1, y1) to the

15. The equation of the polar line of the point (x1, y1 ) w.r.t the conic S = 0 is T = 0

16. The equation of the pair of tangents from the point ( x1 ,  y1 ) to the conic S = 0 ,   S.S1 = T2

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