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Subjects · Leaving Cert Design & Communication Graphics (DCG)

Leaving Cert Design & Communication Graphics (DCG): Hyperbola

How often Hyperbola comes up on the Design & Communication Graphics papers, every year it was asked, and questions to try.

HL Asked on 4 of the last 9 Higher Level papers, most recently in 2023.

Hyperbola, Higher Level(7 marks)

Quick ones on Hyperbola.

(a)The tangent at a point P on a hyperbola bisects which angle?
  1. The external angle between the focal radii
  2. The angle F1PF2 between the focal radii
  3. The angle between PF1 and an asymptote
(b)For any point P on a hyperbola, what does the difference between PF1 and PF2 equal?
  1. The distance between the foci
  2. The conjugate axis
  3. The transverse axis
(c)What are the asymptotes of a hyperbola?
  1. Lines the curve approaches but never meets
  2. The lines joining the two vertices
  3. Lines through the foci square to the axis
Show the answers

(a) The angle F1PF2 between the focal radii

(b) The transverse axis

(c) Lines the curve approaches but never meets

Your turn: Higher Level questions on Hyperbola.

Higher Level

Asked on 4 of the last 9 Higher Level papers, most recently in 2023.

Every paper, year by year

YearWhere it came up
2025Not asked
2024Not asked
2023A2
2022Not asked
2021A2
2019A2, B2
2018Not asked
2017Not asked
2016A3

Links open the State Examinations Commission’s paper for that year.

More Hyperbola questions

Hyperbola, 3 marks

Where does each directrix of a hyperbola lie?

  1. Beyond the focus, on the far side of it from the centre
  2. Through the focus, square to the axis
  3. Between the centre and the nearer vertex
Show the answer

Between the centre and the nearer vertex

The directrix is a ÷ e from the centre. As e > 1, a ÷ e is less than a, so it is inside the vertex. For a = 30 mm and e = 5/3 it is 18 mm from the centre.

Hyperbola, 3 marks

On a hyperbola, distances measured parallel to the asymptotes have a constant product. P gives 10 and 40 mm; Q gives 20 mm and?

  1. 80 mm
  2. 20 mm
  3. 30 mm
Show the answer

20 mm

10 × 40 = 400, so for Q, 20 × ? = 400 and ? = 20 mm. This constant product is how a hyperbola is plotted from its asymptotes and one known point.

Hyperbola, 2 marks

How many branches does a hyperbola have?

  1. Two
  2. One
  3. Four
Show the answer

Two

A hyperbola has two separate mirror-image branches, one round each focus. A plane cutting both nappes of a double cone makes one branch on each.

Other Design & Communication Graphics (DCG) topics

All of Leaving Cert Design & Communication Graphics (DCG)