NCERT Mathematics, Class 11, textbook pages 176–207

How to help your child with Class 11 Maths Chapter 10, Conic Sections, at home

Circles, parabolas, ellipses and hyperbolas, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

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NCERT Class 11 Maths Chapter 10 Conic Sections: what it teaches

Slicing a double cone gives circles, ellipses, parabolas and hyperbolas. Your teen learns their standard equations, foci, vertices and eccentricity, and where they appear in real life.

Why it matters later. Conics appear in physics (orbits), engineering (reflectors) and 3D geometry.

See it: this chapter in pictures

x² + y² − 4x + 6y − 12 = 0(x − 2)² + (y + 3)² = 25centre (2, −3), r = 5
Complete the square.
y² = 8x4a = 8, a = 2focus (2, 0)
Compare with y² = 4ax.
circle e = 0ellipse 0 < e < 1parabola e = 1, hyperbola e > 1
Eccentricity classifies conics.

You need

  • graph paper
  • string and two pins
  • a torch

Tonight’s 45 minutes

  1. Draw an ellipse with string and two pins (the foci).
  2. Shine a torch at a wall at different angles to see ellipses and parabolas.
  3. Find the centre and radius of x² + y² − 4x + 6y − 12 = 0 ((2, −3), 5).
  4. Find the focus of y² = 8x ((2, 0)).

Words to use

  • conic
  • circle
  • parabola
  • ellipse
  • hyperbola
  • focus
  • eccentricity

Watch for

  • Mixing a and b in ellipses. a is the semi-major axis, the larger one.
  • Wrong completing-the-square for circles. Group x and y terms separately.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouFocus of y² = 8x?

Your child4a = 8, a = 2: (2, 0).

A game for this week: String ellipse

  1. Pin two points on cardboard.
  2. Draw ellipses with loops of different lengths.
  3. Measure a and c.
  4. Compute eccentricity.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Planet orbits (ellipses).
  • Dish antennas (parabolas).
  • Cooling towers (hyperbolas).
  • Whispering galleries.

Quick check

Ask these at the end of the week. Tap to see the answer.

Centre and radius of x² + y² − 4x + 6y − 12 = 0?

(2, −3), 5.

Focus of y² = 8x?

(2, 0).

Eccentricity of a circle?

0.

Ready for the next chapter when your child…

  • Identifies conics from equations.
  • Finds centres, foci and vertices.
  • Connects conics to real life.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 11). See the full Class 11 parent guide for every chapter.

Questions parents ask

Why are they called conic sections?

They are slices of a double cone.

Where are parabolas used?

Satellite dishes and headlights.

What is eccentricity?

A measure of how stretched a conic is.