RS Aggarwal Class 11 Chapter 23 Solutions (Ellipse)

RS Aggarwal Solutions for Class 11 Chapter 23 – Ellipse is a perfect study material for students to clear their concepts of Class 11 Maths as it is the base of Class 12 Mathematics. The methods and steps to solve the questions in RS Aggarwal are in a way that becomes easy for students to grasp and helps them in solving all types of questions they come across. The Chapter of RS Aggarwal Solutions becomes easy because of the easy and convenient solutions and methods which are written by industry experts. 

The Chapter consists of 1 exercise with 26 questions in it.  These 26 questions of RS Aggarwal Class 11 Solutions contain all the important topics of the Chapter, which means that if you can solve these 26 questions you have mastered the Chapter. Now the solved examples and the solutions to the questions save your time and make it easy for you to complete the syllabus and moreover resolve all your queries. The benefit of limited questions covering all the concepts is that you can practice again and again and the best part is it is accessible 24*7.

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Important Points of Chapter 23 – Ellipse

  • When the locus of a point in a plane that moves in such a way that the ratio of the distance from a fixed point in the same plane to its distance from a fixed straight line is always constant, then it is known as Ellipse.
  • If the coefficient of x2 has the larger denominator, then its major axis lies along the x-axis, then it is said to be a horizontal ellipse.
  • If centre of the ellipse is (h, k) and the direction of the axes are parallel to the coordinate axes, then its equation is (x – h)2 / a2 + (y – k)2 / b2 = 1
  • The locus of the point of intersection of perpendicular tangents to an ellipse is a director circle. If equation of an ellipse is x2 / a2 + y2 / b2 = 1, then equation of director circle is x2 + y2 = a2 + b2                                                       
  • The equation x = a cos φ, y = b sin φ, taken together are called the parametric equations of the ellipse x2 / a2 + y2 / b2 = 1 , where φ is any parameter
  • The equation of the tangent to the ellipse x2 / a2 + y2 / b2 = 1 at the point (x1, y1) is xx1 / a2 + yy1 / b2 = 1.
  • The points on the ellipse, the normals at which the ellipse passes through a given point are called co-normal points.
  • Two diameters of an ellipse are said to be conjugate diameters if each bisects the chords parallel to the other
  • The common chords of an ellipse and a circle are equally inclined to the axes of the ellipse.
  • The four normals can be drawn from a point on an ellipse.
  • If the equation of parabola has y2 then, the symmetrical axis is along the x-axis and if the equation of parabola has x2, then the symmetrical axis is along the y-axis.

Topics Covered Under Chapter 23 Ellipse

The following different topics are covered under this Chapter:

  • Major and Minor axes
  • Horizontal Ellipse
  • The ordinate and double ordinate
  • A special form of Ellipse
  • Vertical Ellipse
  • Position of a point with respect of Ellipse
  • Parametric equation
  • Equation of chord
  • The eccentric angle of a point
  • Conformal points 
  • Equation of normal
  • Equation of tangent

Important Formulas for Solving Questions 

  • For general form of ellipse: x²/a² + y²/b² = 1

Major Axis: 2a 

Minor Axis: 2b

Vertices: (±a, 0)

Foci: (±c, 0)

Eccentricity: e = c/a

Latus Rectum: 2b²/a

  • For general form of ellipse: x²/b² + y²/a² = 1

Major Axis: 2a 

Minor Axis: 2b

Vertices: (0, ±a)

Foci: (0, ±c)

Eccentricity: e = c/a

Latus Rectum: 2b²/a

Exercise Wise Discussion of RS Aggarwal Class 11 Chapter 23 Ellipse

This exercise 23 has 26 questions in which you have to:

  • Solve the given equations
  • Solve the given equations using formulas
  • Solve the given equations by addition and subtraction
  • Find the equation of ellipse using the given vertices and foci
  • Find the equation of ellipse using the given major and minor axis

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