Chapter 5: Two Dimensional Analytical Geometry-II — Online MCQ Test
MATHS · CLASS 12th · Tamil Nadu State Board
Practice Chapter 5: Two Dimensional Analytical Geometry-II with a free chapter-wise online MCQ test.
This chapter covers: Diving into conic sections this chapter covers equations of circles parabolas ellipses and hyperbolas. It details parametric forms tangents normals and real-world engineering appli....
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter 5: Two Dimensional Analytical Geometry-II — Important Questions & Answers
What is the equation of a circle with centre (0,0) and radius r?
- A. x^2 + y^2 = r^2
- B. x^2 - y^2 = r^2
- C. y^2 = 4ax
- D. x^2 + y^2 = 2r
Answer: A. x^2 + y^2 = r^2
A circle centered at the origin has equation x^2 + y^2 = r^2. This is the standard form of a circle.
A circle centered at the origin has equation x^2 + y^2 = r^2. This is the standard form of a circle.
The standard equation of a parabola opening to the right is:
- A. y^2 = 4ax
- B. x^2 = 4ay
- C. x^2 + y^2 = a^2
- D. x^2 - y^2 = 4a^2
Answer: A. y^2 = 4ax
For a parabola with axis along the x-axis and opening rightward, the standard form is y^2 = 4ax where a > 0.
For a parabola with axis along the x-axis and opening rightward, the standard form is y^2 = 4ax where a > 0.
The equation of the tangent to the circle x^2 + y^2 = r^2 at the point (x1, y1) on the circle is:
- A. xx1 + yy1 = r^2
- B. x + x1 = r^2
- C. y = mx + c
- D. x^2 + y^2 = r
Answer: A. xx1 + yy1 = r^2
The tangent to x^2 + y^2 = r^2 at a point (x1, y1) on the circle is given by xx1 + yy1 = r^2.
The tangent to x^2 + y^2 = r^2 at a point (x1, y1) on the circle is given by xx1 + yy1 = r^2.
The equation x^2 + y^2 - 6x + 8y + 9 = 0 represents a:
- A. Circle
- B. Parabola
- C. Ellipse
- D. Hyperbola
Answer: A. Circle
Since x^2 and y^2 have equal coefficients and the same sign, the equation represents a circle after completing the square.
Since x^2 and y^2 have equal coefficients and the same sign, the equation represents a circle after completing the square.
Which statement is correct for the circle x^2 + y^2 + 2gx + 2fy + c = 0?
- A. Its centre is (-g, -f)
- B. Its centre is (g, f)
- C. Its radius is g + f
- D. Its centre is (-2g, -2f)
Answer: A. Its centre is (-g, -f)
By completing squares, the circle can be written with centre (-g, -f). The constants g and f determine the shift of the center.
By completing squares, the circle can be written with centre (-g, -f). The constants g and f determine the shift of the center.