RS Aggarwal Class 11 Chapter 25 Solutions (Applications of Conic Sections)
RS Aggarwal Solutions for Class 11 Chapter 25 will give you detailed information about the topic- Conic Sections. A Conic Section is a curve obtained as the intersection of the surface of the cone. In the chapter, you will study about the types of Conic Sections like circle, hyperbola, parabola, and ellipse. You will learn about the equations of parabola, circle, ellipse, and hyperbola. Also, you will get to know about their eccentricity, directrix, and focus, etc
This chapter has only 1 exercise with a total of 5 questions. You will have to find different situations as asked in the question. The questions are based on the latest exam pattern. These questions are designed in a manner that if you solve them, it shows that you have a vague understanding of all the concepts of the chapter.
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Topics Discussed in RS Aggarwal Solutions for Class 11 Chapter 25
Conics, (circles, ellipses, parabolas, and hyperbolas) involve a set of curves that are formed by intersecting a plane as well as a double-napped right cone. There are four curves that can be formed. You can graph a Conic Section on a coordinate plane. The Conic Section has some features that include at least one directrix and a focus.
- Vertex: Vertex is an extreme point to a Conic Section.
- Asymptote: Asymptote is a straight line in which a curve approaches arbitrarily closely as it goes to infinity.
- Locus: Locus is the set of all points whose coordinates satisfy a given equation or coordination.
- Focus: Focus is a point that is used to construct and define a Conic Section.
- Nappe: Nappe is one half of a double cone.
- Conic Section: any curve formed by the intersection of a plane with a cone of two nappes.
- Directrix: a line used to construct and define a Conic Section; a parabola has one directrix; ellipses and hyperbola have two (plural: directrices).
When the plane cuts the nappe of the cone, you will have the following situations:
- (a) when =90o, the section is a circle.
- (b) when <<900, the section is an ellipse.
- (c) when =; the section is a parabola.
(In each of the above three situations, the plane cuts entirely across one nappe of the cone).
- (d) when 0<<; the plane cuts through both the nappe and curves of intersection is a hyperbola.
A circle is known as the set of all points in a plane that remains at a constant distance from a fixed point in a plane. The fixed point on a plane in a circle is called the center and the constant distance from the center of the circle is called the radius of the circle.
Equation of a circle in standard form
The equation of a circle with center (h,k) and radius r is given by (x-h)2 + (y-k)2 = r2.
The equation of a circle with center at the origin and radius r is given by x2 + y2 = r2.
General Equation of a Circle
Theorem: The general equation of a circle is of the form x2 + y2 + 2gx + 2fy + c = 0. Also, every equation of form x2 + y2 + 2gx + 2fy + c = 0 represents a circle if (g2 + f2 – c) >0.
A parabola is the set of points P whose distances from a fixed point F in the plane are equal to their distance from a fixed-line i in the plane. F is the fixed point and is called the focus. Whereas, on the other hand, the fixed-line i refers to the Directrix of the parabola.
Under this topic, you will know about the standard equations of the parabola and also how to find the focal distance of a point in a given situation.
An ellipse is the set of points in the plane, the sum of whose distances from two fixed points is constant. The fixed point is called focus, the fixed-line a directrix and the constant ratio () the centricity of the ellipse.
You will know about different topics under the category ellipse:
- Major and Minor axes
- Horizontal Ellipse
- The ordinate and double ordinate
- A special form of Ellipse
- Vertical Ellipse etc.
The hyperbola is the set of all points in the plane, the difference of whose distance from two fixed points is constant. Focus is the fixed point whereas the fixed-line is known as the directrix and the constant ratio denoted by e, the eccentricity of the hyperbola.
You will learn about different topics under this category:
- Transverse and conjugate axes
- Equation of hyperbola in a different form
- Conjugate hyperbola
- Equation of tangent hyperbola
- The focal distance of a point
- Equation of chord etc.
Exercise Wise Discussion of Chapter 25
- This chapter has only one exercise with around 5 questions.
- The questions are entirely based on the latest CBSE exam pattern.
- You will be asked questions from the topic Conic Sections and other subj topics
- Please note that this topic is scoring if you give enough time to practise
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