The document discusses the parabola, a type of conic section. It covers the history of parabolas being discovered by Manaechmus, the tutor of Alexander the Great. Key terms are defined, including focus, directrix, axis, and vertex. The standard equation of a parabola, y2 = 4ax, is derived from the definition and properties. A parabola is then sketched based on this equation.

1. K.J. SOMAIYA COMPREHENSIVE COLLEGE OF EDUCATION TRAINING AND RESEARCH NAME:- S.LAKSHMI R.NO:- 55 TOPIC:- CONIC SECTION (PARABOLA)

2. CONTENT HISTORY DEFINITION IMPORTANT TERMS STANDARD EQUATION OF PARABOLA DERIVATION SKETCHING OF A PARABOLA EVALUATION SOLUTION

3. HISTORY Discovered by the Greek mathematician Manaechmus. He was the tutor of the great Alexander. The theory applies to the Lenses of Telescopes. Microscopes. Weather prediction. Communication by Satellites. Construction of buildings and bridges .

4. DEFINITION A conic section is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line. Note:- Fixed Point -> Focus Fixed Line -> Directrix Constant Ratio -> Eccentricity ( e )

5. P ( MOVING POINT ) S ( FIXED POINT ) M L K D I R E C T R I X Meaning of conic section through diagram

6. IMPORTANT TERM AXIS :- The straight line passing through the focus and perpendicular to the directrix is called Axis. M B A S P

7. IMPORTANT TERM 2) VERTEX :- A point of intersection of a conic with its axis is called a Vertex. M A P1 B S P2 P3

8. STANDARD EQUATION OF A PARABOLA y 2 =4ax S (a,0) P (x,y) A (0,0) Z(-a,0) X Y T

9. DERIVATION focus- S(a,0) vertex A(0,0) directrix LM AX - +ve Axis AY- +ve Axis Moving point P(x,y) By definition PS = PM √ (x-a) 2 +(y-0) 2 = x+a (x-a) 2 +y 2 = (x+a) 2 x 2 + a 2 -2ax + y 2 = x 2 + a 2 + 2ax y 2 = 4ax

10. SKETCHING OF PARABOLA -5a -4a -3a -2a 5a 4a 3a 2a a -a -a -2a -3a -4a -5a a 2a 3a 4a 5a 4a -4a -2a 2a 0 Y 4a 4a a a 0 X

11. EVALUATION Q1. Define the following terms. Conic section Axis Vertex Q2. Tick the correct answer. Who discovered Conic Section? a) Manaechmus b) Alexander ANS - a

12. EVALUATION The fixed point is known as a) Vertex b) Focus ANS - b

13. THANK YOU