Important Terms Related to Parabola in Coordinate Geometry
2 D Co-ordinate Geometry
Lecture-9
Parabola
UG (B.Sc., Part-1)
By
Dr. Md. Ataur Rahman
Guest Faculty
Department of Mathematics
M.L. Arya, College, Kasba
PURNEA UNIVERSITY, PURNIA
Important terms related to Parabola
Important terms related to Parabola
Axis of Parabola
:-The line passing through the
focus and perpendicular to the directrix is
called axis of parabola.
In the above given figure,
the line ZS is the axis of parabola.
Vertex:
-The point of intersection of the parabola
and axis of parabola is called its vertex.
In the above given figure,
A is the vertex of parabola.
Important terms related to Parabola
Chord:-
The line segment joining any two points
on the parabola is chord of the parabola.
Focal chord:-
The chord passing through the
focus focus (S) is called focal chord of the
parabola.
In the given figure, PQ is a focal chord.
Focal distance:-
The distance of any point on the
parabola from the focus is called focal distance
of the parabola. i.e PS is the focal distance.
Important terms related to Parabola
Latus rectum:-
A chord passing through the focus
and perpendicular to the axis of parabola is
latus rectum of the parabola.
In the given figure,
LL’ is the latus rectum.
Doule ordinate:-
A chord perpendicular to the
axis of parabola is called axis of the parabola.
Explanation of
Explanation of
1. Focus
2. Vertex
3. Equation of directrix
Since
Z (-a,0), then
4.
Axis of parabola
Since x-axis is perpendicular to the directrix.
5.
Tangent at the vertex:- y-axis i.e
x=0
Explanation
6.
End points of Latus rectum:-
7.
Length of latus rectum
and its equation is
8. Focal distance from any point P(x,y)
Learn about key concepts related to the parabola in coordinate geometry including the axis of the parabola, vertex, chord, focal chord, focal distance, latus rectum, and more. This comprehensive guide covers definitions, properties, and equations associated with parabolas, providing a solid foundation for further study in the subject.
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Presentation Transcript
2 D Co-ordinate Geometry Lecture-9 Parabola UG (B.Sc., Part-1) By Dr. Md. Ataur Rahman Guest Faculty Department of Mathematics M.L. Arya, College, Kasba PURNEA UNIVERSITY, PURNIA
Important terms related to Parabola Axis of Parabola:-The line passing through the focus and perpendicular to the directrix is called axis of parabola. In the above given figure, the line ZS is the axis of parabola. Vertex:-The point of intersection of the parabola and axis of parabola is called its vertex. In the above given figure, A is the vertex of parabola.
Important terms related to Parabola Chord:- The line segment joining any two points on the parabola is chord of the parabola. Focal chord:-The chord passing through the focus focus (S) is called focal chord of the parabola. In the given figure, PQ is a focal chord. Focal distance:- The distance of any point on the parabola from the focus is called focal distance of the parabola. i.e PS is the focal distance.
Important terms related to Parabola Latus rectum:-A chord passing through the focus and perpendicular to the axis of parabola is latus rectum of the parabola. In the given figure, LL is the latus rectum. Doule ordinate:-A chord perpendicular to the axis of parabola is called axis of the parabola.
Explanation of = 2 4 , 0 y ax a
Explanation of = 2 4 , 0 y ax a 1. Focus 2. Vertex 3. Equation of directrix Since Z (-a,0), then 4. Axis of parabola Since x-axis is perpendicular to the directrix. y = ( ,0) a (0,0) A S = + = . 0 x a iex a 0 5. Tangent at the vertex:- y-axis i.e x=0
Explanation 6. End points of Latus rectum:- ( ,2 ) L ( , 2 ) a = = a a and L a + 0 = = 4 LL OL OL a 7. Length of latus rectum and its equation is 8. Focal distance from any point P(x,y) = . x a ie x a = = + PS a x
