Conic Sections

Maths · Class 11

Simulation · Maths · Class 11

A hyperbola keeps a constant difference

"A hyperbola keeps a constant difference" is a free, interactive Class 11 Maths simulation for JEE, built on the NCERT section "Hyperbola: foci and axes" in Conic Sections. A point P on a hyperbola with PF₁ and PF₂ drawn; their difference stays 2a. The box a × b and the foci at c show c² = a² + b² next to the ellipse's c² = a² − b². JEE Main asked 116 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).

From the lesson Hyperbola: foci and axes in Conic Sections. Change the values and watch what happens.

A hyperbola keeps a constant differenceMaths · Class 11

What it shows

NCERT §10.6, §10.6.1, §10.6.2

A point P on a hyperbola with PF₁ and PF₂ drawn; their difference stays 2a. The box a × b and the foci at c show c² = a² + b² next to the ellipse's c² = a² − b².

Controls

4 to try

  • Slidera 1–5
  • Sliderc a–7
  • SliderP along the branch
  • Togglecompare with ellipse

Try this

Set foci (±5, 0) and vertices (±3, 0); read b = 4, e = 5/3 and check |PF₁ − PF₂| = 6 at any P.

Common mistake

Using c² = a² − b² for a hyperbola; quoting e < 1.

In JEE Main

42 shifts analysed

116 questions from Conic Sections across the 42 JEE Main shifts Lumi has analysed (2017–2026).

See the past questions

The idea behind it

NCERT §10.6, §10.6.1

  • A hyperbola is the set of all points of a plane for which the difference of the distances from two fixed points, the foci, is a constant. 'Difference' means the distance to the farther focus minus the distance to the nearer one.
  • The mid-point of the foci is the centre. The line through the foci is the transverse axis and the line through the centre perpendicular to it is the conjugate axis. The hyperbola meets the transverse axis at its two vertices.
  • The distance between the foci is 2c and between the vertices 2a (the length of the transverse axis). The quantity b is defined by b = √(c² − a²), and 2b is the length of the conjugate axis.
  • Taking P at a vertex shows that the constant difference is exactly 2a, the distance between the vertices.
  • Eccentricity e = c/a, as for the ellipse. Since c is at least a, e is never less than 1, and each focus is ae from the centre.
  • Compare the ellipse: there c² = a² − b² and e < 1; for the hyperbola c² = a² + b² and e > 1. Mixing these two relations is the commonest slip in this chapter.

Questions

4 answers

What does the "A hyperbola keeps a constant difference" simulation show?
A point P on a hyperbola with PF₁ and PF₂ drawn; their difference stays 2a. The box a × b and the foci at c show c² = a² + b² next to the ellipse's c² = a² − b².
What mistake does the "A hyperbola keeps a constant difference" simulation fix?
A common mistake it clears up: using c² = a² − b² for a hyperbola; quoting e < 1.
Does JEE Main ask questions from Conic Sections?
Yes. JEE Main asked 116 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Hyperbola: foci and axes" in Conic Sections (Class 11 Maths).

Embed this simulation

Free, with a link back

Teaching this idea? Put the simulation on your own page or LMS with this code.