To get the equation of a conic in terms of and , we use a property, known as the focus-directrix property.
Let there be a fixed line (The Directrix) and a fixed point (The Focus). Let be a point on the locus of conic and let be perpendicular to . Clearly, as moves, slides on . Now, consider the ratio
If we do not allow this ratio to change, 4 possibilities arise, giving us distinct shapes:
Axis of a conic is the line about which a conic is symmetric. A conic may have 1 or 2 or more axes of symmetry.
Vertex of a conic is the point of intersection of the conic with the axis.
Chord is any line segment, which joins 2 points on a curve. If the chord passes through the focus, it is known as focal chord.
Focal length is the length of segment which joins a point on the conic to the focus.
Latus rectum is the focal chord which is perpendicular to the axis.
Center of a conic is the point which bisects every chord of the conic passing through it.
Double ordinate of a conic is any chord, which is perpendicular to the axis.