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Subjects · Leaving Cert Design & Communication Graphics (DCG)

Leaving Cert Design & Communication Graphics (DCG): Parabola

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

HL Asked on 7 of the last 9 Higher Level papers, most recently in 2025. most years

OL Asked on 5 of the last 9 Ordinary Level papers, most recently in 2024.

Parabola, Higher Level(7 marks)

Quick ones on Parabola.

(a)What is the eccentricity of a parabola?
  1. Between 0 and 1
  2. Exactly 1
  3. Greater than 1
(b)Why are satellite dishes and car headlight reflectors parabolic?
  1. The curve has the same curvature at every point
  2. Rays parallel to the axis reflect through the vertex
  3. Rays parallel to the axis reflect through the focus
(c)In the rectangle method for a parabola, how are the half-width and the depth of the rectangle divided?
  1. Into the same number of equal parts
  2. In proportion to the squares
  3. In the ratio 1 : 3 : 5
Show the answers

(a) Exactly 1

(b) Rays parallel to the axis reflect through the focus

(c) Into the same number of equal parts

Your turn: Higher Level questions on Parabola.

Higher Level

Asked on 7 of the last 9 Higher Level papers, most recently in 2025. most years

Every paper, year by year

YearWhere it came up
2025B1
2024Not asked
2023Not asked
2022A2
2021B1
2019B2
2018A3
2017A2, B1
2016B2

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

More Parabola questions

Parabola, 3 marks

The ordinate from P meets a parabola's axis 30 mm from the vertex. Where does the tangent at P cross the axis?

  1. At the focus
  2. 15 mm from the vertex, inside the curve
  3. 30 mm beyond the vertex, outside the curve
Show the answer

30 mm beyond the vertex, outside the curve

The vertex bisects the subtangent: the tangent meets the axis as far outside the vertex as the ordinate's foot is inside it. Join P to that point for the tangent.

Parabola, 2 marks

Which conic has only one focus and one directrix?

  1. The hyperbola
  2. The parabola
  3. The ellipse
Show the answer

The parabola

The ellipse and hyperbola each have two foci and two directrices, one pair on each side of the centre. The parabola has no centre and a single focus and directrix.

Parabola, 3 marks

Tangents are drawn at the two ends of a focal chord of a parabola. Where do they meet, and at what angle?

  1. On the directrix, at 90°
  2. At the focus, at 60°
  3. At the vertex, at 45°
Show the answer

On the directrix, at 90°

Tangents at the ends of any focal chord cross at right angles on the directrix. For the latus rectum each is at 45° to the axis, so they meet where the directrix crosses the axis.

Ordinary Level

Asked on 5 of the last 9 Ordinary Level papers, most recently in 2024.

Every paper, year by year

YearWhere it came up
2025Not asked
2024A1
2023Not asked
2022A2
2021A1
2019A3
2018Not asked
2017A2
2016Not asked

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

More Parabola questions

Parabola, 3 marks

To draw a parabola in a rectangle, how are the half-base and the side divided?

  1. In the ratio 1 to 3 to 5
  2. Into parts that shrink towards the vertex
  3. Into the same number of equal parts
Show the answer

Into the same number of equal parts

Equal parts on each: lines from the vertex to the side divisions cross the lines from the base divisions at points on the curve.

Parabola, 3 marks

The focus is 20 mm from the directrix. How far is the vertex from the focus?

  1. 40 mm
  2. 10 mm
  3. 20 mm
Show the answer

10 mm

The vertex is on the curve, so it is as far from the focus as from the directrix. It sits halfway: 20 divided by 2 = 10 mm.

Parabola, 3 marks

The tangent at a point P on a parabola bisects the angle between PF and…

  1. The perpendicular from P to the directrix
  2. The axis of the parabola, through F
  3. The directrix itself, extended
Show the answer

The perpendicular from P to the directrix

Join P to the focus F, and draw PM at 90 degrees to the directrix. The tangent bisects angle FPM; the normal is at 90 degrees to the tangent.

Other Design & Communication Graphics (DCG) topics

All of Leaving Cert Design & Communication Graphics (DCG)