Conic Sections Formulas

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Conic Section is a part of a cone. It is obtained when a 3 dimensional cone is cut. The intersection may be a

circle, ellipse, parabola, hyperbola or even a line, point, or line. The conic section is the intersection of a

plane and a cone. The conic section is a curve or a right circular conical surface. The general formula for the

conic section:

Ax^2+Bxy+CY^2+Dx+Ey+F = 0

The kind of section is decided from calculating B^2 – 4AC.

Example 1: An ice-cream cone is cut into a section. The B^2 – 4AC is equal to zero. What will be

the conic section?

Solution: The general conic formula is Ax^2+Bxy+Cy^2+Dx+Ey+F = 0

For the given problem the value of B^2 – 4AC helps us find out the type of conic section curve we get. In the

given problem B^2 – 4AC is equal to zero. This means the conic section will be either a parabola, 2 parallel

lines, 1 line or no curve.

Example 2: What will be the type of conic section for the equation 4px = y^2. Also what will be its

eccentricity and relation to focus?

Solution: For every conic section it has a specific equation, eccentricity and relation to focus.  In the given

problem equation of parabola having horizontal vertex has its equation as 4px = y^2. Its relation with focus is

that the distance from vertex to focus is p and p = p. The eccentricity is c/a, where c is distance from center

to focus.

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