1.
Topic : Parabola

2.
 Definition: A parabola is a set of all points in a plane
that are equidistant from a fixed line and a
fixed point (not on the line) in the plane.
'Para' means 'for'
'Bola' means 'throwing'
Parabola means shape describe
when we throw a ball in the air.

3.
 The fixed line is called directrix of the parabola and fixed point f is called
focus.
 Latus rectum is a line segment perpendicular to the axis of parabola
through the focus and whose end points lie on the parabola.
Key Terms
 A point of intersection of a conic with its axis is
called vertex.
 The line passing through the focus and
perpendicular to the directrix is called axis.
 The constant ratio is called eccentricity denoted
with the letter e.

4.
Deriving standard equation of a parabola

5.
Latus rectum is a line
segment perpendicular to
the axis of parabola
through the focus and
whose end points lie on the
parabola.
Length of latus rectum = 4a

6.
Types of parabola : 1) Right-open parabola
Vertex: (0,0)
Focus: (a,0)
Axis: Y=0
Equation of directrix: x = -a
Length of latus rectum = 4a
𝒚𝟐 = 𝟒𝒂𝒙

7.
y
2) Find the equation of the parabola
with focus (2,0), directrix x=-2.
𝑦2
= 12𝑥
1)

8.
2) Left-open parabola
Vertex: (0,0)
Focus: (-a,0)
Axis: Y=0
Equation of directrix: x = a
Length of latus rectum = 4a
𝒚𝟐 = −𝟒𝒂𝒙

9.
2) Find the equation of the parabola
with vertex (0,0) and directrix x=8.
1) 𝑦2
= 15𝑥

10.
3) Open-upwards parabola
Vertex: (0,0)
Focus: (0,a)
Axis: X=0
Equation of directrix: y = -a
Length of latus rectum = 4a
𝒙𝟐 = 𝟒𝒂𝒚

11.
2) Find the equation of the parabola
with vertex (0,0) and directrix y=-9.
1) 𝑥2
= 5𝑦

12.
4) Open-downward parabola
Vertex: (0,0)
Focus: (0,-a)
Axis: X=0
Equation of directrix: y = a
Length of latus rectum = 4a
𝒙𝟐
= −𝟒𝒂𝒚

13.
Applications
 The parabola has many important applications, from a
parabolic antenna or parabolic microphone to
automobile headlight reflectors and the design of
ballistic missiles.
 It is frequently used in physics, engineering, and many
other areas.

14.
Parabola with 𝒚𝟐
term Parabola with 𝒙𝟐 term
Symmetrical about X-axis. Symmetrical about Y-axis.
Axis is along the X-axis. Axis is along the Y-axis.
It open right handed when co-
efficient of ‘x’ is positive and
left handed when co-efficient
of ‘x’ is negative.
It opens upwards if co-
efficient of ‘y’ is positive and
downwards if co-efficient of
‘y’ is negative.

15.
 Indian track and field athlete Neeraj Chopra, who
competes in the javelin throw, won a gold medal
at Tokyo Olympics. He is the first track and field
athlete to win a gold medal for India at the
Olympics.
 Based on above information, answer the following
1. Name the shape of paths followed by javelin.
2. If the equation of such a curve is given by 𝑥2
= −16𝑦, then
write the coordinate of foci.
3. Write the equation of directrix and length of semi-latus rectum.
Case Study