Introduction to Conic Sections A conic section is


























- Slides: 26

Introduction to Conic Sections

A conic section is a curve formed by the intersection of _____________ a plane and a double cone.



Circles The set of all points that are the same distance from the center. Standard Equation: With CENTER: (h, k) & RADIUS: r (square root) (h , k) r



Ellipse Basically an ellipse is a squished circle Standard Equation: (h , k) a b Center: (h , k) a: major radius (horizontal), length from center to edge of circle b: minor radius (vertical), length from center to top/bottom of circle * You must square root the denominator


The Ellipse • Tilt a glass of water and the surface of the liquid acquires an elliptical outline. • Salami is often cut obliquely to obtain elliptical slices which are larger.

• On a far smaller scale, the electrons of an atom move in an approximately elliptical orbit with the nucleus at one focus.

• Any cylinder sliced on an angle will reveal an ellipse in cross-section • (as seen in the Tycho Brahe Planetarium in Copenhagen).


Example This must equal 1 a² b Center: (-4 , 5) a: 5 b: 2 2

vertex Parabola We’ve talked about this before… a U-shaped graph vertex Standard Equations: OR This equation opens up or down This equation opens left or right HOW DO YOU TELL…LOOK FOR THE SQUARED VARIABLE Vertex: (h , k) • If there is a negative in front of the squared variable, then it opens down or left. • If there is NOT a negative, then it opens up or right.



• The easiest way to visualize the path of a projectile is to observe a waterspout. • Each molecule of water follows the same path and, therefore, reveals a picture of the curve.

Hyperbolas What I look like…two parabolas, back to back. Standard Equations: OR This equation opens left and right This equation opens up and down Have I seen this before? Sort of…only now we have a minus sign in the middle Center: (h , k)







Introduction to conic sections
Introduction to conic sections
Vertex in real life
Rotating conic sections
Lesson 1 exploring conic sections
Example of parabola in real life
Parabola vs hyperbola
Types of conic sections
Conic sections
Completing the square ellipse
Chapter 9 conic sections and analytic geometry
Conic sections graphing calculator
Conics cheat sheet
Conic sections equations
How to identify conic sections from general form
Conic sections quiz
Classifying conic sections worksheet answers
Equation for hyperbola
Type of conic
Polar equation of conic
Engineering curves
Real life application of conic sections
Identifying conic sections
Ellipse terminology
Polar equation
Conic sections in polar coordinates
Conic sections