Chapter Exam

Unit 2: Transformation of Axes — Online MCQ Test

Q: The formula for translation of axes from old coordinates (x, y) to new coordinates (X, Y) with origin shifted to (h, k) is:

Answer: A. x = X - h, y = Y - k — If the new origin is at (h, k), then the old coordinates are given by x = X + h and y = Y + k, or equivalently X = x - h and Y = y - k. The correct direct substitution is x = X + h, y = Y + k, so here the option written as x = X - h is not correct. Wait—this must be corrected: the correct relation in terms of old coordinates is x = X + h, y = Y + k.

Q: If the axes are rotated by 90°, what are the values of cosθ and sinθ respectively?

Answer: B. 0 and 1 — For θ = 90°, cos 90° = 0 and sin 90° = 1. These values are often used in substitution during rotation problems.

Q: Which equation can be simplified to remove the xy-term by rotating the axes?

Answer: B. x^2 + 4xy + y^2 = 0 — An xy-term indicates that the conic is not aligned with the coordinate axes. Rotation of axes is used to eliminate the mixed term 4xy.

Q: For the equation ax^2 + 2hxy + by^2 = 0, the condition for the axes to be already aligned with the conic is:

Answer: A. h = 0 — If h = 0, the mixed term disappears and no rotation is needed. The quadratic form is already in axes-aligned form.

MATHEMATICS - 1B · CLASS 11 INTERMEDIATE 1 YEAR · Telangana State Board

Practice Unit 2: Transformation of Axes with a free chapter-wise online MCQ test for Telangana State Board CLASS 11 INTERMEDIATE 1 YEAR MATHEMATICS - 1B. This chapter covers: This chapter covers translation of axes rotation of axes and finding new transformed equations of curves after shifting or rotating coordinate axes.. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Unit 2: Transformation of Axes — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 11 INTERMEDIATE 1 YEAR MATHEMATICS - 1B — Unit 2: Transformation of Axes, with answers and explanations. These are sample questions; the exam has its own separate question set.

In a translation of axes, if the origin is shifted to a new point (h, k) without changing the direction of the axes, which statement is correct?

A. Only the origin changes, directions of axes remain the same ✓
B. Only the x-axis changes its direction
C. Both axes rotate by the same angle
D. The curve always changes its degree

Answer: A. Only the origin changes, directions of axes remain the same
In translation of axes, the coordinate axes are shifted parallel to themselves. Only the origin changes; the directions of axes do not change.

The formula for translation of axes from old coordinates (x, y) to new coordinates (X, Y) with origin shifted to (h, k) is:

A. x = X - h, y = Y - k ✓
B. x = X + h, y = Y + k
C. X = x + h, Y = y + k
D. X = x - h, Y = y - k

Answer: A. x = X - h, y = Y - k
If the new origin is at (h, k), then the old coordinates are given by x = X + h and y = Y + k, or equivalently X = x - h and Y = y - k. The correct direct substitution is x = X + h, y = Y + k, so here the option written as x = X - h is not correct. Wait—this must be corrected: the correct relation in terms of old coordinates is x = X + h, y = Y + k.

If the axes are rotated by 90°, what are the values of cosθ and sinθ respectively?

A. 1 and 0
B. 0 and 1 ✓
C. -1 and 0
D. 0 and -1

Answer: B. 0 and 1
For θ = 90°, cos 90° = 0 and sin 90° = 1. These values are often used in substitution during rotation problems.

Which equation can be simplified to remove the xy-term by rotating the axes?

A. x^2 + y^2 = 1
B. x^2 + 4xy + y^2 = 0 ✓
C. x + y = 1
D. x^2 - y^2 = 0

Answer: B. x^2 + 4xy + y^2 = 0
An xy-term indicates that the conic is not aligned with the coordinate axes. Rotation of axes is used to eliminate the mixed term 4xy.

For the equation ax^2 + 2hxy + by^2 = 0, the condition for the axes to be already aligned with the conic is: