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Subjects · Leaving Cert Design & Communication Graphics (DCG)

Leaving Cert Design & Communication Graphics (DCG): Ellipse

How often Ellipse 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 2025.

OL Asked on 4 of the last 9 Ordinary Level papers, most recently in 2025.

Ellipse, Higher Level(8 marks)

Quick ones on Ellipse.

(a)The tangent at a point P on an ellipse bisects which angle?
  1. The internal angle between the focal radii
  2. The external angle between the focal radii
  3. The angle between PF1 and the major axis
(b)For any point P on an ellipse with foci F1 and F2, what does PF1 + PF2 equal?
  1. The distance F1F2
  2. The minor axis
  3. The major axis
(c)To locate the foci from the axes, an arc of what radius is drawn from an end of the minor axis?
  1. Half the major axis
  2. The full major axis
  3. Half the minor axis
Show the answers

(a) The external angle between the focal radii

(b) The major axis

(c) Half the major axis

Your turn: Higher Level questions on Ellipse.

Higher Level

Asked on 4 of the last 9 Higher Level papers, most recently in 2025.

Every paper, year by year

YearWhere it came up
2025A2
2024B2
2023Not asked
2022Not asked
2021Not asked
2019Not asked
2018Not asked
2017B1
2016B2

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

More Ellipse questions

Ellipse, 3 marks

In the trammel method for an ellipse, what distances are marked on the strip from the tracing point?

  1. The full lengths of the major and minor axes
  2. The two focal distances from the centre
  3. Half the major and half the minor axis
Show the answer

Half the major and half the minor axis

As the two marks slide along the axes the tracing point stays on the ellipse. The marks are set at the semi-minor and semi-major lengths from the point.

Ellipse, 2 marks

An ellipse has an eccentricity close to 0. What is its shape like?

  1. Almost a parabola
  2. Almost a circle
  3. Long and very thin
Show the answer

Almost a circle

e = c ÷ a. Near 0 the foci are close to the centre and the two axes almost equal; a circle is the limit, e = 0. As e nears 1 the ellipse becomes long and thin.

Ellipse, 3 marks

Concentric circle method, major axis horizontal: how is each point on the ellipse found?

  1. Down from the outer circle, across from the inner
  2. Across from the outer circle, down from the inner
  3. Where a radius cuts the outer circle
Show the answer

Down from the outer circle, across from the inner

Each radius cuts the major-axis circle and the minor-axis circle. A vertical from the outer cut meets a horizontal from the inner cut at a point on the ellipse.

Ordinary Level

Asked on 4 of the last 9 Ordinary Level papers, most recently in 2025.

Every paper, year by year

YearWhere it came up
2025A2
2024Not asked
2023A1
2022Not asked
2021Not asked
2019Not asked
2018A1
2017Not asked
2016A1

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

More Ellipse questions

Ellipse, 2 marks

What is the eccentricity of an ellipse?

  1. Exactly 1
  2. Greater than 1
  3. Less than 1
Show the answer

Less than 1

Each point on an ellipse is nearer the focus than the directrix, so distance to focus divided by distance to directrix is below 1.

Ellipse, 2 marks

For any point on an ellipse, the two distances to the foci add up to what?

  1. The distance between the foci
  2. The major axis
  3. The minor axis
Show the answer

The major axis

This is the key property of the ellipse. A loop of string around two pins at the foci, pulled tight by a pencil, traces an ellipse.

Ellipse, 2 marks

In the auxiliary circles method, the two circles have diameters equal to…

  1. The major and minor axes
  2. The two focal distances
  3. The major axis and the focal chord
Show the answer

The major and minor axes

Draw concentric circles on the two axes. Radial lines cut both; lines from these cuts parallel to the axes meet at points on the ellipse.

Other Design & Communication Graphics (DCG) topics

All of Leaving Cert Design & Communication Graphics (DCG)