maths class 11 conic sections

1. Maths project
Class - 11
Circle ellipse parabola hyperbola
Done by
R.Praveen class 11 –‘A’
Topic: Conic sections

2. •Parabola
A parabola is a curve where any point is at an equal distancefrom:
1) a fixed point (the focus ), and
2) a fixed straight line (the directrix )
• Equations
• Place the parabola on the cartesian coordinates (x-y graph) with:
• its vertex at the origin "O" and
• its axis of symmetry lying on the x-axis,
• then the curve is defined by: y2 = 4ax

3. The equations of parabolas in different orientations are as
follows:
y2 = 4ax y2 = -4ax x2 = 4ay x2 = -4ay
Latus rectum
latus rectum = 4a

4. USES:
So the parabola can be used for:
• satellite dishes,
• radar dishes,
• concentrating the sun's rays to make a hot
spot,
• the reflector on spotlights and torches,
• etc

5. Ellipse
An ellipse usually looks like a squashed circle.
An ellipse is the set of all points on a plane whose distance
from two fixed points F and G add up to a constant.
Equation
By placing an ellipse on an x-y graph (with its major axis on the x-axis and minor axis on the y-
axis), the equation of the curve is:
x2/a2 + y2/b2 = 1

6. Hyperbola
A hyperbola is a curve where the distances of any point from:
a fixed point (the focus), and
a fixed straight line (the directrix) are always in the same ratio.

7. Equation
By placing a hyperbola on an x-y graph (centered over
the x-axis and y-axis), the equation of the curve is:
x2/a2 − y2/b2 = 1

8. Latus Rectum
The Latus Rectum is the line through the focus
and parallel to the directrix.
The length of the Latus Rectum is 2b2/a.
Eccentricity
We already mentioned the eccentricity (usually shown as the letter e), it shows how "uncurvy"
(varying from being a circle) the hyperbola is.
It can also given by the formula:
e =

9. Thank
you