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# Mini parabola

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K J Somiaya Comprehensive College of education. PPT presentation of CAP

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### Mini parabola

1. 1. K.J. SOMAIYA COMPREHENSIVE COLLEGE OF EDUCATION TRAINING AND RESEARCH NAME:- S.LAKSHMI R.NO:- 55 TOPIC:- CONIC SECTION (PARABOLA)
2. 2. CONTENT <ul><li>HISTORY </li></ul><ul><li>DEFINITION </li></ul><ul><li>IMPORTANT TERMS </li></ul><ul><li>STANDARD EQUATION OF PARABOLA </li></ul><ul><li>DERIVATION </li></ul><ul><li>SKETCHING OF A PARABOLA </li></ul><ul><li>EVALUATION </li></ul><ul><li>SOLUTION </li></ul>
3. 3. HISTORY <ul><li>Discovered by the Greek mathematician Manaechmus. </li></ul><ul><li>He was the tutor of the great Alexander. </li></ul><ul><li>The theory applies to the </li></ul><ul><ul><li>Lenses of Telescopes. </li></ul></ul><ul><ul><li>Microscopes. </li></ul></ul><ul><ul><li>Weather prediction. </li></ul></ul><ul><ul><li>Communication by Satellites. </li></ul></ul><ul><ul><li>Construction of buildings and bridges . </li></ul></ul>
4. 4. DEFINITION <ul><li>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. </li></ul><ul><li>Note:- Fixed Point -> Focus </li></ul><ul><li> Fixed Line -> Directrix </li></ul><ul><li> Constant Ratio -> Eccentricity ( e ) </li></ul>
5. 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. 6. IMPORTANT TERM <ul><li>AXIS :- The straight line passing through the focus and perpendicular to the directrix is called Axis. </li></ul>M B A S P
7. 7. IMPORTANT TERM <ul><li>2) VERTEX :- A point of intersection of a conic with its axis is called a Vertex. </li></ul>M A P1 B S P2 P3
8. 8. STANDARD EQUATION OF A PARABOLA <ul><li> y 2 =4ax </li></ul>S (a,0) P (x,y) A (0,0) Z(-a,0) X Y T
9. 9. DERIVATION <ul><li>focus- S(a,0) vertex A(0,0) </li></ul><ul><li>directrix LM </li></ul><ul><li>AX - +ve Axis AY- +ve Axis </li></ul><ul><li>Moving point P(x,y) </li></ul><ul><li>By definition PS = PM </li></ul><ul><li>√ (x-a) 2 +(y-0) 2 = x+a </li></ul><ul><li>(x-a) 2 +y 2 = (x+a) 2 </li></ul><ul><li>x 2 + a 2 -2ax + y 2 = x 2 + a 2 + 2ax </li></ul><ul><li>y 2 = 4ax </li></ul>
10. 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. 11. EVALUATION <ul><li>Q1. Define the following terms. </li></ul><ul><li>Conic section </li></ul><ul><li>Axis </li></ul><ul><li>Vertex </li></ul><ul><li>Q2. Tick the correct answer. </li></ul><ul><li>Who discovered Conic Section? </li></ul><ul><li>a) Manaechmus </li></ul><ul><li>b) Alexander </li></ul><ul><li>ANS - a </li></ul>
12. 12. EVALUATION <ul><li>The fixed point is known as </li></ul><ul><li>a) Vertex </li></ul><ul><li>b) Focus </li></ul><ul><li>ANS - b </li></ul>
13. 13. THANK YOU