Conics - Ellipse

What You'll Learn

Identify ellipse equations in conic ready form and distinguish them from other conics

Determine the center, vertices, and co-vertices of an ellipse from its equation

Calculate the major and minor axes lengths using denominators in the standard form

Locate the foci using the ellipse formula c² = a² - b²

Calculate eccentricity to measure how far an ellipse deviates from being circular

Apply the conic definition: sum of distances from any point to foci equals major axis length

What You'll Practice

Converting ellipse equations to conic ready form with squared denominators

Sketching ellipses by plotting center, radii, vertices, and co-vertices

Finding foci coordinates on the major axis using a, b, and c values

Calculating eccentricity values and interpreting ellipse shapes

Why This Matters

Understanding ellipses is essential for astronomy, physics, and engineering, where planetary orbits, satellite paths, and optical systems all follow elliptical patterns. Mastering ellipse equations builds your analytical geometry skills and prepares you for calculus and advanced applications in science and technology.

Before You Start — Make Sure You Can:

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)Pythagorean identities

This Unit Includes

2 Video lessons

Practice exercises

Skills

Ellipses

Conic Sections

Major Axis

Minor Axis

Foci

Vertices

Eccentricity

Standard Form

OH Curriculum Aligned