The locus of a point in the plane that moves such that its distance from a fixed point (focus) is in a constant ratio to its distance from a fixed line (directrix) is a .
This is the alternative definition of a conic! The constant ratio between the distance from a focus and the distance from a directrix is called an eccentricity. For different values of eccentricity, we get different conics.
Eccentricity, e
Conic Section
0< e< 1
Ellipse
e=1
Parabola
e> 1
Hyperbola
Finally, let's fill in the blank!
The locus of a point in the plane that moves such that its distance from a fixed point (focus) is in a constant ratio to its distance from a fixed line (directrix) is a conic.
