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
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