Unit 1: Circle — Online MCQ Test
MATHEMATICS - 2B · CLASS 12 INTERMEDIATE 2 YEAR · Telangana State Board
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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....
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Unit 1: Circle — Important Questions & Answers
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.
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).
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).
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.
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?
- A. c = 0
- B. a = 0
- C. b = 0
- D. a = b
Answer: A. c = 0
Since the origin lies on the circle, substituting x = 0 and y = 0 gives c = 0.
Since the origin lies on the circle, substituting x = 0 and y = 0 gives c = 0.