For hyperbola x²/16−y²/9=1, slopes of asymptotes are:
- ±16/9
- ±4/3
- ±9/16
- ±3/4
Show answer and explanation
Answer: D. ±3/4
Slopes = ±b/a = ±3/4.
FSC Mathematics: Conic Sections, questions with answers
Practise 46 real Federal Board questions on Conic Sections from 2023 to 2026. See the answer and explanation as soon as you answer.
46real questions
18multiple choice
5exam sessions
About Conic Sections in FSC Mathematics
Conic Sections is one of the 14 main chapters in our Federal Board FSC Mathematics question bank (12th class), and about 10% of its real questions come from it. Tayyari Karo has 46 real questions on this chapter from 2023 to 2026; 18 are multiple choice and marked instantly, and the rest are short and long questions with a model answer. By difficulty: 23 medium, 16 hard, 7 easy.
Work through the questions below, then open the explanation for each one. Redo the ones you missed a few days later.
Try 8 real questions
These are real past-paper questions. Think of your answer first, then open the explanation.
The equation of circle with centre (1,1) and radius 2 is:
- (x+1)²+(y+1)²=2
- (x+1)²+(y+1)²=4
- (x−1)²+(y−1)²=2
- (x−1)²+(y−1)²=4
Show answer and explanation
Answer: D. (x−1)²+(y−1)²=4
(x−h)²+(y−k)²=r², r²=4.
Find the length of tangent drawn from (10,5) to the circle x²+y²=125
- 5
- 10
- 15
- 0
Show answer and explanation
Answer: D. 0
Length²=10²+5²−125=0 ⇒ length=0 (point lies on the circle).
The ellipse x²/a²+y²/b²=1 becomes a circle when:
- a<b
- a>b
- a=b
- a=0
Show answer and explanation
Answer: C. a=b
Equal semi-axes give a circle.
Directrices of the hyperbola x²/a²−y²/b²=1 are:
- x=0
- y=0
- x=±a/e
- y=±e/a
Show answer and explanation
Answer: C. x=±a/e
For a hyperbola with transverse axis along x, the directrices are the vertical lines x=±a/e.
What is the length of the latus rectum of the parabola x² = 4ay?
- a
- 4a
- 2a
- 8a
Show answer and explanation
Answer: B. 4a
For x² = 4ay, the length of the latus rectum is 4a (the coefficient of y).
Check whether the line y=2x+1 intersects, touches, or misses the circle x²+y²=5.
Show model answer
Substitute: x²+(2x+1)²=5 ⇒ 5x²+4x−4=0
Discriminant = 16+80 = 96 > 0
Two distinct real roots ⇒ the line intersects the circle at two points.
Find equation of tangent to the hyperbola (2/3)x²−(3/5)y²=1 at point (3√6/2, 5/3).
Show model answer
Standard form: x²/(3/2) − y²/(5/3) = 1, so A=3/2, B=5/3
Tangent at (x₁,y₁): (x·x₁)/A − (y·y₁)/B = 1
(2x₁/3)x − (3y₁/5)y = 1, with x₁=3√6/2, y₁=5/3:
2x₁/3 = √6, 3y₁/5 = 1
√6·x − y = 1
Sessions with Conic Sections questions
| Session | Questions |
|---|---|
| 2026 Annual | 8 |
| 2025 1st Annual | 8 |
| 2025 2nd Annual | 11 |
| 2024 Annual | 11 |
| 2023 Annual | 8 |
Common questions
What does the Conic Sections chapter cover on this page?
46 real Federal Board (FBISE) Mathematics questions on Conic Sections from 2023 to 2026, for 12th class. Each one shows the session it came from.
Are the answers official?
No. We could not find an official FBISE marking scheme for these papers, so the answers and explanations are written by Tayyari Karo for practice. Check anything important with your teacher or textbook.
Is it free?
You can start free with no signup. A small set of papers per subject is free, and Premium unlocks the full question bank.
Other Mathematics chapters
- Differentiation 61
- Vectors 46
- Integration 39
- Functions and Limits 31
- Trigonometric Identities 30
- Matrices and Determinants 29
- Sequences and Series 28
- Introduction to Analytic Geometry 28
- Fundamentals of Trigonometry 26
- Quadratic Equations 21
- Binomial Theorem 20
- Permutation/Combination/Probability 19
- Number Systems 17