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# Maths PPT on parabola Class 11.pptx

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# Maths PPT on parabola Class 11.pptx

PPT on Parabola class 11 Maths.

PPT on Parabola class 11 Maths.

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### Maths PPT on parabola Class 11.pptx

1. 1. Topic : Parabola
2. 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. 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. 4. Deriving standard equation of a parabola
5. 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. 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. 7. y 2) Find the equation of the parabola with focus (2,0), directrix x=-2. 𝑦2 = 12𝑥 1)
8. 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. 9. 2) Find the equation of the parabola with vertex (0,0) and directrix x=8. 1) 𝑦2 = 15𝑥
10. 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. 11. 2) Find the equation of the parabola with vertex (0,0) and directrix y=-9. 1) 𝑥2 = 5𝑦
12. 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. 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. 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. 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