NUST NET Maths chapter 10: Maths · Analytic geometry MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

30 exam-style questions on Maths · Analytic geometry, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

30 questions · 3 topics · 10 per test

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What chapter 10 covers

Ten Maths · Analytic geometry questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. The distance between the points (−1, 2) and (5, −6) is

  1. A
    10
  2. B
    14
  3. C
    4√2
  4. D
    100
Show answer

Answer: A. √[(5 + 1)2 + (−6 − 2)2] = √(36 + 64) = √100 = 10. Adding the coordinates instead of subtracting them gives 4√2.

2. The tangent to the circle x2 + y2 = 25 at the point (3, 4) is

  1. A
    3x + 4y = 25
  2. B
    4x − 3y = 0
  3. C
    4x + 3y = 25
  4. D
    3x + 4y = 5
Show answer

Answer: A. The tangent to x2 + y2 = a2 at (x1, y1) is xx1 + yy1 = a2, here 3x + 4y = 25. The line 4x − 3y = 0 is the radius through (3, 4), i.e. the normal.

3. The radius of the circle 2x2 + 2y2 − 8x + 12y + 8 = 0 is

  1. A
    3
  2. B
    2√11
  3. C
    √17
  4. D
    9
Show answer

Answer: A. Divide by 2 first: x2 + y2 − 4x + 6y + 4 = 0, so r = √(4 + 9 − 4) = 3. Skipping the division gives 2√11.

4. The vertex of the parabola y2 − 4y − 8x + 12 = 0 is

  1. A
    (2, 1)
  2. B
    (1, 2)
  3. C
    (−1, 2)
  4. D
    (1, −2)
Show answer

Answer: B. Complete the square: y2 − 4y + 4 = 8x − 8, i.e. (y − 2)2 = 8(x − 1), so the vertex is (1, 2).

5. The centre and radius of the circle x2 + y2 − 6x + 4y − 12 = 0 are

  1. A
    (−3, 2) and 5
  2. B
    (3, −2) and 1
  3. C
    (3, −2) and 5
  4. D
    (6, −4) and 5
Show answer

Answer: C. Complete the squares: (x − 3)2 + (y + 2)2 = 12 + 9 + 4 = 25, so the centre is (3, −2) and the radius is 5. Radius 1 comes from subtracting the 12 instead of adding it.

6. Which point lies in the solution region of 2x + 3y ≤ 12, x ≥ 0, y ≥ 0?

  1. A
    (5, 1)
  2. B
    (2, 3)
  3. C
    (3, 2)
  4. D
    (0, 5)
Show answer

Answer: C. (3, 2) gives 6 + 6 = 12 ≤ 12, which is true (points on the boundary line count). The others give 13, 13 and 15, all greater than 12.

7. The acute angle between the lines y = 3x + 1 and y = −2x + 5 is

  1. A
    30°
  2. B
    60°
  3. C
    45°
  4. D
    90°
Show answer

Answer: C. tan θ = |(m1 − m2)/(1 + m1m2)| = |(3 + 2)/(1 − 6)| = 1, so θ = 45°.

8. The line y = x + c touches the circle x2 + y2 = 8 when c equals

  1. A
    ±2√2
  2. B
    ±4
  3. C
    ±8
  4. D
    ±2
Show answer

Answer: B. For tangency the distance from the centre (0, 0) to x − y + c = 0 equals the radius: |c|/√2 = 2√2, so c = ±4. (Equivalently c2 = r2(1 + m2) = 16.)

9. The equation of the line through (2, −1) with gradient 3 is

  1. A
    3x − y + 7 = 0
  2. B
    x − 3y − 5 = 0
  3. C
    3x + y − 5 = 0
  4. D
    3x − y − 7 = 0
Show answer

Answer: D. y + 1 = 3(x − 2) gives y = 3x − 7, i.e. 3x − y − 7 = 0. The line x − 3y − 5 = 0 passes through the point but has gradient 1/3.

10. The lines 2x + ky = 5 and 3x − 4y = 1 are perpendicular when k equals

  1. A
    3/2
  2. B
    −3/2
  3. C
    8/3
  4. D
    −8/3
Show answer

Answer: A. The gradients are −2/k and 3/4. Perpendicular: (−2/k)(3/4) = −1, so k = 3/2. k = −8/3 makes the gradients equal, which gives parallel lines.

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Ways to practise this chapter

Maths · Analytic geometry: questions students ask

How many Maths · Analytic geometry MCQs are there?

30, each with the answer and a short explanation, across 3 topics: Straight lines, Circles and conic sections, Linear inequalities and linear programming. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 10 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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