NCERT Solutions for Class 11 Maths Chapter 11

Download NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections शंकु परिच्छेद in PDF form. Students can do directly 12th class after doing 10th though NIOS Admission 2018-19. For the other subjects, there are also available NCERT Books Solutions to free download without any login password. These are applicable for all CBSE & UP Board (intermediate) students for their March 2019 exams.


NCERT Solutions for Class 11 Maths Chapter 11

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Class 11 Maths Chapter 11 Conic Sections Solutions




Important Terms on Conic Sections

  • Circle, ellipse, parabola and hyperbola are curves which are obtained by intersection of a plane and cone in different positions
  • Circle: It is the set of all points in a plane that are equidistant from a fixed point in that plane.
  • Parabola: It is the set of all points in a plane which are equidistant from a fixed point (focus) and a fixed line in the plane. Fixed point does not lie on the line.
    • Latus Rectum: A chord through focus perpendicular to axis of parabola is called its latus rectum.
  • Ellipse: It is the set of points in a plane the sum of whose distances from two fixed points in the plane is a constant and is always greater than the distances between the fixed points.
  • Hyperbola: It is the set of all points in a plane, the differences of whose distance from two fixed points in the plane is a constant.



Important Extra Questions with Answers on Conic Sections
  1. Find the centre and radius of the circle x² + y² – 6x + 4y – 12 = 0. [Answer: (3, -2), 5]
  2. Find the equation of hyperbola satisfying given conditions foci (5, 0) and transverse axis is of length 8. [Answer: x²/16 – y²/9 = 1.]
  3. Find the coordinates of points on parabola y² = 8x whose focal distance is 4. [Answer: (2, 4), (2, -4)]
  4. If one end of a diameter of the circle x² + y² – 4x – 6y + 11 = 0 is (3, 4), then find the coordinates of the other end of diameter. [Answer: (1, 2)]
  5. Find equation of an ellipse having vertices (0, 5) and foci (0, 4). [Answer: x²/9 + y²/25 = 1]
  6. Find the equation of a circle whose centre is at (4, –2) and 3x – 4y+ 5 = 0 is tangent to circle. [Answer: x² + y² – 8x + 4y – 5 = 0]
  7. If the distance between the foci of a hyperbola is 16 and its eccentricity is 2, then obtain the equation of a hyperbola. [Answer: x² – y² = 32]
  8. If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity. [Answer: e = √3/2]



Try These
  • Find the length of major and minor axis of the following ellipse, 16x² + 25y² = 400. [Answer: 10, 8]
  • Find equation of circle concentric with circle 4x² + 4y² – 12x – 16y – 21 = 0 and of half its area. [Answer: 2x² + 2y² – 6x + 8y + 1 = 0]
  • Find the equation for the ellipse that satisfies the given condition Major axis on the x-axis and passes through the points (4, 3) and (6, 2). [Answer: x²/52 + y²/13 = 1]


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