Parabola: focus, directrix and latus rectum: Class 11 practice
y² = 4ax opens right with focus (a, 0), directrix x = −a and latus rectum 4a. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Coordinate geometry basics
The idea behind parabola: focus, directrix and latus rectum
y² = 4ax opens right with focus (a, 0), directrix x = −a and latus rectum 4a. x² = 4ay opens up with focus (0, a) and directrix y = −a. A negative a flips the direction.
Step-by-step method
- Match the equation to y² = 4ax or x² = 4ay.
- Find a.
- Write focus, directrix and latus rectum length.
Worked example 1 (Basic)
For y² = 24x, find the focus, directrix and length of latus rectum.
- 4a = 24 → a = 6
- Focus (6, 0), directrix x = -6
- Latus rectum = 24
- Answer: Focus (6, 0); x = -6; LR 24
Worked example 2 (Standard)
For x² = 4y, find the focus and directrix.
- 4a = 4 → a = 1
- Focus (0, 1), directrix y = -1
- Answer: Focus (0, 1); y = -1
Worked example 3 (Challenge)
For y² = -24x, find the focus, directrix and length of latus rectum.
- 4a = -24 → a = -6
- Focus (-6, 0), directrix x = 6
- Latus rectum = 24
- Answer: Focus (-6, 0); x = 6; LR 24
Common mistakes and misconceptions
- Confusing the axis of the parabola
- Latus rectum taken as 2a
Practice questions
- (Basic) For y² = 4x, find the focus, directrix and length of latus rectum.
- (Basic) For y² = 8x, find the focus, directrix and length of latus rectum.
- (Standard) For x² = 20y, find the focus and directrix.
- (Standard) For x² = 16y, find the focus and directrix.
- (Challenge) For y² = -12x, find the focus, directrix and length of latus rectum.
- (Challenge) For y² = -16x, find the focus, directrix and length of latus rectum.
Answer key with full working
- Q1: 4a = 4 → a = 1 → Focus (1, 0), directrix x = -1 → Latus rectum = 4 → Answer: Focus (1, 0); x = -1; LR 4
- Q2: 4a = 8 → a = 2 → Focus (2, 0), directrix x = -2 → Latus rectum = 8 → Answer: Focus (2, 0); x = -2; LR 8
- Q3: 4a = 20 → a = 5 → Focus (0, 5), directrix y = -5 → Answer: Focus (0, 5); y = -5
- Q4: 4a = 16 → a = 4 → Focus (0, 4), directrix y = -4 → Answer: Focus (0, 4); y = -4
- Q5: 4a = -12 → a = -3 → Focus (-3, 0), directrix x = 3 → Latus rectum = 12 → Answer: Focus (-3, 0); x = 3; LR 12
- Q6: 4a = -16 → a = -4 → Focus (-4, 0), directrix x = 4 → Latus rectum = 16 → Answer: Focus (-4, 0); x = 4; LR 16
Syllabus note
This skill is listed under "Conic Sections" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is parabola: focus, directrix and latus rectum in?
"Conic Sections", Class 11 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.