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Exploring Conics Sections can be a very confusing lesson if you let it be. The best advice I can give to any teacher is to start with the basics of the equation of a circle. Make sure they have mastered h,k form and how changes to the equation transform the shape.
Once you are confident they completely understand moving a circle around the coordinate plane algebraically then use an app like Geogebra.org to let them play with transforming the circle on their own. This will allow them to play with the equation and see side by side how the shape changes with the change in h,k. They will also be able to see ellipses and hyperbolas for the first time through experimentation rather than through awful drawings on the chalkboard ðŸ™‚
Here are some Excellent Video Resources to help you with your lessons on Conic Sections. This is one of the longest lessons of the Algebra 2 course and one conic build off the next. Make sure their foundation is solid or Hyperbolas will be a nightmare ðŸ™‚
Where Do Conic Sections Come From?
How to Create Circles with Geogebra:
RealWorld Experiments for Conic Discovery:
Teaching the Algebra of a Circle:
Teaching the Algebra of a Parabola:
Teaching the Algebra of an Ellipse:
Teaching the Algebra of a Hyperbola:
Possibilities using Geogebra:
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