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Questions and Answers

Conic Section

circle, e=0, parabola, e=1 ellipse, e<1, hyperbola, e>1.

Ax²+Bxy+Cy²+Dx+Ey+F=0

Circle, A=C, Parabola, A=0 or C=0, Ellipse, A≠C, same sign, Hyperbola, A≠C, diff sign, Signup and view all the answers

B²-4AC Signup and view all the answers

ellipse or circle Signup and view all the answers

parabola Signup and view all the answers

Hyperbola Signup and view all the answers

Circle, A=C, Ellipse A≠C Signup and view all the answers

Focus of point Signup and view all the answers

line Signup and view all the answers

focus Signup and view all the answers

denoted by "e" (constant) Signup and view all the answers

Study Notes

A conic section is formed by the intersection of a double-napped cone and a plane.
The angle and position of the intersecting plane determine the type of conic section produced (circle, ellipse, parabola, or hyperbola).

The eccentricity (e) measures how much a conic section deviates from being circular.
Eccentricity values:
- e = 0 corresponds to a circle.
- 0 < e < 1 corresponds to an ellipse.
- e = 1 corresponds to a parabola.
- e > 1 corresponds to a hyperbola.

The general quadratic equation of conic sections is given by:
- Ax² + Bxy + Cy² + Dx + Ey + F = 0.
A, B, C, D, E, and F are constants.

The quadratic terms refer to Ax², Bxy, and Cy² in the general equation.
The coefficients A, B, and C play crucial roles in identifying the type of conic section represented.

The discriminant for conic sections is defined as:
- D = B² - 4AC.
This formula helps classify the conic section based on the values of A, B, and C.

To determine whether a conic section is an ellipse or circle:
- Check the coefficients A and C:
  - If A = C and B = 0, the conic is a circle.
  - If A ≠ C and B = 0, the conic is an ellipse.