lecture #6 analytic geometry
TRANSCRIPT
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Lecture #6
• Parabola• Parts of Parabola• Equations of Parabola with center at origin• Equations of parabola with center at (h, k)• Graph of Parabola
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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.
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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)
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PARTS OF PARABOLA
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GRAPHS OF PARABOLAThe graph of parabola if the vertex is at the origin,
and opens to the right,
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The graph of parabola if the vertex is at the origin, and opens to the left,
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The graph of parabola if the vertex is at the origin, and opens upward,
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The graph of parabola if the vertex is at the origin, and opens downward,
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The graph of parabola if the vertex is at (h, k) , and opens to the right,
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The graph of parabola if the vertex is at (h, k) , and opens to the left,
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The graph of parabola if the vertex is at (h, k) , and opens upward,
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The graph of parabola if the vertex is at (h, k) , and opens downward,
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EQUATIONS OF PARABOLAIf the parabola opens to the right, with vertex at the
origin, the equation is
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If the parabola opens to the left, with vertex at the origin, the equation is
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If the parabola opens upward, with vertex at the origin, the equation is
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If the parabola opens downward, with vertex at the origin, the equation is
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If the parabola opens to the right, with vertex at (h, k), the equation is
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If the parabola opens to the left, with vertex at (h, k), the equation is
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If the parabola opens upward, with vertex at (h, k), the equation is
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If the parabola opens downward, with vertex at (h, k), the equation is
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The general equation of parabola is given by
Or
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FORMULAS
VERTEX AT (0, 0 ) FOCUS DIRECTRIX
ENDS OF LATUS
RECTUM
LENGTH OF LATUS RECTUM
EQUATION OF
PARABOLA
RIGHT
LEFT
UPWARD
DOWNWARD
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FORMULAS
VERTEX AT (h, k) FOCUS DIRECTRIX
ENDS OF LATUS
RECTUM
LENGTHOF
LATUS RECTUM
EQUATION OF PARABOLA
RIGHT
LEFT
UPWARD
DOWNWARD
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Sample ProblemFind the vertex, focus, length of the latus rectum, ends of the latus rectum and hence graph the parabola.