Menu

Conic Sections

NCERT Class 11 Mathematics Chapter 10

Conic Sections for Class 11 Maths and JEE: circle, parabola, ellipse and hyperbola, their standard equations, eccentricity and latus rectum.

6 topics Updated 8 Nov 2026

For: Class 11 and JEE, unless a topic says otherwise

In the syllabus: JEE Class 11 syllabus

With your textbook

NCERT Mathematics (Class 11), Chapter 10 “Conic Sections”, reprint 2026-27.

Open the official NCERT chapter (PDF, 3.0 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Sections of a cone

    How a plane cutting a double cone gives a circle, ellipse, parabola or hyperbola, degenerate cases and eccentricity.

    NCERT Sections 10.1–10.2 12 min read 4 solved examples 9 practice questions

  2. Circle

    (x − h) + (y − k) = r, the general form, centre and radius, and all of NCERT Exercise 10.1 solved.

    NCERT Section 10.3 14 min read 6 solved examples 12 practice questions

  3. Circle on a diameter and a line meeting a circle

    Diameter form of circle for JEE Main: the circle on given ends of a diameter, where a line meets a circle, the condition of tangency and chord length.

    JEE only 12 min read 5 solved examples 10 practice questions

  4. Parabola

    Focus and directrix, the four standard equations, latus rectum 4a and focal distance, with solved NCERT examples.

    NCERT Section 10.4 14 min read 6 solved examples 19 practice questions

  5. Ellipse

    Foci, axes, a = b + c, eccentricity c/a, standard equations and latus rectum 2b/a, with solved NCERT examples.

    NCERT Section 10.5 16 min read 6 solved examples 23 practice questions

  6. Hyperbola

    Foci, axes, c = a + b, eccentricity c/a, latus rectum 2b/a, ellipse vs hyperbola, with solved NCERT examples.

    NCERT Section 10.6 15 min read 6 solved examples 14 practice questions

Key formulas in this chapter

Sections of a cone

  • β = 90°: circle
  • α < β < 90°: ellipse
  • β = α: parabola
  • 0° ≤ β < α: hyperbola
  • through the vertex: point, line or pair of intersecting lines
  • e = cos β / cos α (plane not through vertex, 0° < α < 90°)

Circle

  • (x − h) + (y − k) = r
  • x + y = r
  • x + y + 2gx + 2fy + c = 0: centre (−g, −f), radius √(g + f − c)
  • inside / on / outside: CP < r, = r, > r

Circle: diameter form and a line

  • (x − x)(x − x) + (y − y)(y − y) = 0
  • y = mx + c meets x + y = r twice, once or never as c <, =, > r(1 + m)
  • tangent: y = mx ± r√(1 + m)
  • chord length = 2√(r − d)

Parabola

  • y = 4ax: focus (a, 0), directrix x = −a
  • y = −4ax: focus (−a, 0), directrix x = a
  • x = 4ay: focus (0, a), directrix y = −a
  • x = −4ay: focus (0, −a), directrix y = a
  • latus rectum = 4a
  • y = ±4ax: PF = a + |x|; x = ±4ay: PF = a + |y|

Ellipse

  • x/a + y/b = 1, a > b: foci (±c, 0)
  • x/b + y/a = 1, a > b: foci (0, ±c)
  • a = b + c
  • e = c/a, 0 < e < 1
  • latus rectum = 2b/a
  • PF = a + ex, PF = a − ex (foci on the x-axis)

Hyperbola

  • x/a − y/b = 1: foci (±c, 0), vertices (±a, 0)
  • y/a − x/b = 1: foci (0, ±c), vertices (0, ±a)
  • c = a + b
  • e = c/a > 1
  • latus rectum = 2b/a
  • asymptotes (JEE) of x/a − y/b = 1: y = ±(b/a)x

More in Mathematics