Circles and Conic Sections

​Introduction to Conic Sections

Multiple Choice

These are two-dimensional curves made by the intersection of a plane and a double right circular cone. What are these?

• Plane figures

• Undefined geometrical figures

• Conic Sections

• Double-napped cone

​Introduction to Conic Sections

• Conic Sections were discovered and have been largely studied during the classical Greek period, 600 to 300 BCE.

• Conic Sections, simply known as "conics", are two-dimensional curves made by the intersection of a plane and double right circular cone.

Multiple Choice

Aside from Circle, what are the other types of conic sections?

• Plane and cones

• Parabola, Ellipse, and Hyperbola

• Double right circular cone

• Point and line

The four types of Conic Sections are the Circle, Parabola, Ellipse and Hyperbola.

Multiple Choice

What is being formed when the plane passes through the vertex of the double circular cone?

• Degenerate Conic

• Conic figure

• Hyperbola

• Curve

Multiple Choice

These are examples of Degenerate Conics, EXCEPT:

• Point

• Line

• Intersecting Lines

• Triangle

​Degenerate Conics

• If the plane passes through the vertex of the double right circular cone, the conic sections formed are called degenerate conics.

Multiple Choice

What is the general quadratic formula used to represent a conic section parallel to the axes?

• $$Ax^2+𝐵𝑥𝑦+Cy^2+𝐷𝑥+𝐸𝑦+𝐹=0$$  

• $$ax^2+bx+c=0$$  

• $$Ax^2+Cy^2+Dx+Ey+F=0$$  

• $$ax^2+by^2=c^2$$  

General equation of Conics