High School · Expressing Geometric Properties with Equations

CCSS.MATH.CONTENT.HSG.GPE.A.3

(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

Read this standard on the official Common Core site

Lessons that teach this standard

• Conic Sections in General Form

  Tell a circle, ellipse, parabola and hyperbola apart from Ax² + Cy² + Dx + Ey + F = 0, then complete the square to find the center, radius, vertices and axes.

• Ellipses and Hyperbolas from Their Foci

  Why an ellipse is every point whose distances to two foci add to a constant, how squaring twice turns that into x²/a² + y²/b² = 1, and how the hyperbola follows.