Chapter Exam

Unit 1: Circle — Online MCQ Test

Q: What is the standard equation of a circle with centre (0,0) and radius r?

Answer: A. x^2 + y^2 = r^2 — A circle centered at the origin has equation x^2 + y^2 = r^2, where r is the radius.

Q: In the general equation x^2 + y^2 + 2gx + 2fy + c = 0, the centre of the circle is:

Answer: B. (-g, -f) — Comparing with the standard form, the centre is (-g, -f).

Q: The centre of the circle x^2 + y^2 - 8x + 10y + 9 = 0 is:

Answer: C. (4, -5) — For x^2 + y^2 + 2gx + 2fy + c = 0, centre is (-g, -f). Here 2g = -8 and 2f = 10, so centre is (4, -5).

Q: The tangent to the circle x^2 + y^2 - 2x - 4y - 4 = 0 at point (4,0) is:

Answer: A. 2x + y = 8 — The centre is (1,2). The radius to (4,0) has slope -2/3, so the tangent slope is 3/2. Using point-slope form gives 2x + y = 8.

Q: A circle has equation x^2 + y^2 + 2ax + 2by + c = 0 and passes through the origin. Which of the following is true?

Answer: A. c = 0 — Since the origin lies on the circle, substituting x = 0 and y = 0 gives c = 0.

MATHEMATICS - 2B · CLASS 12 INTERMEDIATE 2 YEAR · Telangana State Board

Practice Unit 1: Circle with a free chapter-wise online MCQ test for Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2B. This chapter covers: This chapter covers standard equation of a circle general equation position of a point center radius equations of tangents normals length of tangent power of a point and chord of c.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Unit 1: Circle — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2B — Unit 1: Circle, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the standard equation of a circle with centre (0,0) and radius r?

A. x^2 + y^2 = r^2 ✓
B. (x - h)^2 + (y - k)^2 = r
C. x^2 - y^2 = r^2
D. x + y = r^2

Answer: A. x^2 + y^2 = r^2
A circle centered at the origin has equation x^2 + y^2 = r^2, where r is the radius.

In the general equation x^2 + y^2 + 2gx + 2fy + c = 0, the centre of the circle is:

A. (g, f)
B. (-g, -f) ✓
C. (2g, 2f)
D. (-2g, -2f)

Answer: B. (-g, -f)
Comparing with the standard form, the centre is (-g, -f).

The centre of the circle x^2 + y^2 - 8x + 10y + 9 = 0 is:

A. (8, -10)
B. (-8, 10)
C. (4, -5) ✓
D. (-4, 5)

Answer: C. (4, -5)
For x^2 + y^2 + 2gx + 2fy + c = 0, centre is (-g, -f). Here 2g = -8 and 2f = 10, so centre is (4, -5).

The tangent to the circle x^2 + y^2 - 2x - 4y - 4 = 0 at point (4,0) is:

A. 2x + y = 8 ✓
B. x + 2y = 8
C. 4x + y = 8
D. x - 2y = 8

Answer: A. 2x + y = 8
The centre is (1,2). The radius to (4,0) has slope -2/3, so the tangent slope is 3/2. Using point-slope form gives 2x + y = 8.

A circle has equation x^2 + y^2 + 2ax + 2by + c = 0 and passes through the origin. Which of the following is true?