Class 11 Mathematics — Chapter 10: CONIC SECTIONS

What you'll learn

• ▸Introduction to Conic Sections
• ▸Standard Equation of a Circle
• ▸Finding Center and Radius from General Equation
• ▸Definition of a Parabola
• ▸Standard Equations of a Parabola
• ▸Degenerate Conic Sections

Chapter Summary

--- PAGE 1 --- Chapter 10 CONIC SECTIONS ❖ Let the relation of knowledge to real life be very visible to your pupils and let them understand how by knowledge the world could be transformed. – BERTRAND RUSSELL ❖ 10.1 Introduction In the preceding Chapter 10, we have studied various forms of the equations of a line. In this Chapter, we shall study about some other curves, viz., circles, ellipses, parabolas and hyperbolas. The names parabola and hyperbola are given by Apollonius. These curves are in fact, known as conic sections or more commonly conics because they can be obtained as intersections of a plane with a double napped right circular cone. These curves have a very wide range of applications in fields such as planetary motion, design of telescopes and antennas, reflectors in flashlights and automobile headlights, etc. Now, in the subsequent sections we will see how the intersection of a plane with a double napped right circular results in different types of curves. 10.2 Secti…

Practice Questions from this Chapter

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1. Show real-world conic sections. Get Solution →
2. Explain cone's connection to shapes. Get Solution →
3. List practical uses for parabolas. Get Solution →
4. According to the text, who gave the names 'parabola' and 'hyperbola' to the conic sections? Get Solution →
5. What is the name for the fixed point from which all points on a circle are equidistant? Get Solution →
6. When a plane intersects a cone such that the angle β made with the vertical axis is 90°, what conic section is formed? Get Solution →
7. What is the fixed line in the definition of a parabola called? Get Solution →
8. What is the general equation of a circle with center (h, k) and radius r? Get Solution →

Did you know?

• 💡 All planets orbit the sun in elliptical paths, not perfect circles.
• 💡 A thrown ball follows a perfect parabolic curve through the air.
• 💡 Hyperbolic curves help calculate positions for long-range navigation systems.
• 💡 The first discovery of conic sections dates back to ancient Greek mathematicians.
• 💡 The "eye" of a hurricane often forms a nearly perfect circular shape.

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