3. ๏ถ 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.
4. ๏ 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.
6. 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
7.
8. 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
๐๐ = ๐๐๐
9. y
2) Find the equation of the parabola
with focus (2,0), directrix x=-2.
๐ฆ2
= 12๐ฅ
1)
10. 2) Left-open parabola
Vertex: (0,0)
Focus: (-a,0)
Axis: Y=0
Equation of directrix: x = a
Length of latus rectum = 4a
๐๐ = โ๐๐๐
11. 2) Find the equation of the parabola
with vertex (0,0) and directrix x=8.
1) ๐ฆ2
= 15๐ฅ
12. 3) Open-upwards parabola
Vertex: (0,0)
Focus: (0,a)
Axis: X=0
Equation of directrix: y = -a
Length of latus rectum = 4a
๐๐ = ๐๐๐
13. 2) Find the equation of the parabola
with vertex (0,0) and directrix y=-9.
1) ๐ฅ2
= 5๐ฆ
14. 4) Open-downward parabola
Vertex: (0,0)
Focus: (0,-a)
Axis: X=0
Equation of directrix: y = a
Length of latus rectum = 4a
๐๐
= โ๐๐๐
15.
16. 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.
17. Parabola with ๐๐
term Parabola with ๐๐ 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 โxโ is positive and
left handed when co-efficient
of โxโ is negative.
๏It opens upwards if co-
efficient of โyโ is positive and
downwards if co-efficient of
โyโ is negative.
18. ๏ถ 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 ๐ฅ2
= โ16๐ฆ, then
write the coordinate of foci.
3. Write the equation of directrix and length of semi-latus rectum.
Case Study