CONIC SECTIONS

Conic
Sections

PRE-CALCULUS

LEARNING OBJECTIVES:

❑ Understand how Conics are formed.

❑ Identify the different types of Conics.

❑ Give the equation of Conics.

❑ Make graphs of the different Conics

What are Conics?

➢Conics are

sections formed
when a double-
napped cone is
sliced through a
plane

CIRCLE

➢ Circle can be formed when the intersecting plane is parallel to the

base of the cone

PARABOLA

➢ Parabola can be formed if the cutting plane is parallel to the edge

of the cone.

ELLIPSE

➢ If the cutting plane is slightly tilted so as to make closed figure,

then an ellipse is formed.

HYPERBOLA

➢ To obtain a hyperbola, the cutting plane must be positioned at a

steeper angle.

NON DEGENERATE CONICS

➢These conics are

also referred to as
non-degenerate
conics. A non-
degenerate conic is
a conic formed
when the cutting
plane does not
pass the vertex of
the cone.

DEGENERATE CONICS

➢When the plane

intersects the
vertex of the
cone, degenerate
conics are
formed. The
degenerate conics
are point, line and
intersecting lines.

POINT

➢ Point can be formed if the plane parallel to the base of the cone

intersects with its vertex.

LINE

➢ Line can be obtained when the plane intersects the vertex of the

cone and its tangent to it.

CROSSED LINES

➢ Two intersecting lines can be formed when the plane passes

through the vertex and through both cones.

➢ References

https://roblulham.wordpress.com/2019/08/19/conic-section-
gif/

https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_
%28Apex%29/09%3A_Curves_in_the_Plane/9.01%3A_Conic_Se
ctions

Aspuria. C., Manalo. L., & Molina, M., (2017). Pre-Calculus For
Senior High School. Mutya Publishing House, Inc.. Potrero,
Malabon City