Lecture #6

• Parabola• Parts of Parabola• Equations of Parabola with center at origin• Equations of parabola with center at (h, k)• Graph of Parabola

PARABOLALocus of points such that the distance from a point to

the focus is equal to the distance from the same point and the directrix.

PARTS OF PARABOLA Vertex – sharpest turn point of the parabola. (represented

by V) Focus – a point which is used to determine or define the

parabola. (represented by F) Latus Rectum – a line passing through the focus,

perpendicular to the axis of symmetry, and it has two endpoints.

Directrix – a line perpendicular to axis of symmetry (represented by D)

Axis of symmetry – a line that divides the parabola in half Eccentricity – the eccentricity of the parabola is always

equal to one. (represented by e)

PARTS OF PARABOLA

GRAPHS OF PARABOLAThe graph of parabola if the vertex is at the origin,

and opens to the right,

The graph of parabola if the vertex is at the origin, and opens to the left,

The graph of parabola if the vertex is at the origin, and opens upward,

The graph of parabola if the vertex is at the origin, and opens downward,

The graph of parabola if the vertex is at (h, k) , and opens to the right,

The graph of parabola if the vertex is at (h, k) , and opens to the left,

The graph of parabola if the vertex is at (h, k) , and opens upward,

The graph of parabola if the vertex is at (h, k) , and opens downward,

EQUATIONS OF PARABOLAIf the parabola opens to the right, with vertex at the

origin, the equation is

If the parabola opens to the left, with vertex at the origin, the equation is

If the parabola opens upward, with vertex at the origin, the equation is

If the parabola opens downward, with vertex at the origin, the equation is

If the parabola opens to the right, with vertex at (h, k), the equation is

If the parabola opens to the left, with vertex at (h, k), the equation is

If the parabola opens upward, with vertex at (h, k), the equation is

If the parabola opens downward, with vertex at (h, k), the equation is

The general equation of parabola is given by

Or

FORMULAS

VERTEX AT (0, 0 ) FOCUS DIRECTRIX

ENDS OF LATUS

RECTUM

LENGTH OF LATUS RECTUM

EQUATION OF

PARABOLA

RIGHT

LEFT

UPWARD

DOWNWARD

FORMULAS

VERTEX AT (h, k) FOCUS DIRECTRIX

ENDS OF LATUS

RECTUM

LENGTHOF

LATUS RECTUM

EQUATION OF PARABOLA

RIGHT

LEFT

UPWARD

DOWNWARD

Sample ProblemFind the vertex, focus, length of the latus rectum, ends of the latus rectum and hence graph the parabola.