Chapter Exam

Chapter 5: Two Dimensional Analytical Geometry-II — Online MCQ Test

Q: What is the 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. This is the standard form of a circle.

Q: The standard equation of a parabola opening to the right is:

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.

Q: The equation of the tangent to the circle x^2 + y^2 = r^2 at the point (x1, y1) on the circle is:

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.

Q: The equation x^2 + y^2 - 6x + 8y + 9 = 0 represents a:

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.

Q: Which statement is correct for the circle x^2 + y^2 + 2gx + 2fy + c = 0?

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.

MATHS · CLASS 12th · Tamil Nadu State Board

Practice Chapter 5: Two Dimensional Analytical Geometry-II with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 12th MATHS. 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.

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Chapter 5: Two Dimensional Analytical Geometry-II — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 12th MATHS — Chapter 5: Two Dimensional Analytical Geometry-II, with answers and explanations. These are sample questions; the exam has its own separate question set.

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.

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.

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 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.

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.