Chapter Exam

Unit 3: Parabola — Online MCQ Test

Q: What is the standard equation of a parabola with vertex at the origin and axis along the positive x-axis?

Answer: A. y^2 = 4ax — For a parabola opening to the right with vertex at the origin, the standard form is y^2 = 4ax.

Q: In the parabola y^2 = 4ax, the focus is at:

Answer: A. (a, 0) — The parabola y^2 = 4ax has focus at (a, 0) and directrix x = -a.

Q: If a point P lies on the parabola y^2 = 4ax with parametric coordinate t, then P is:

Answer: A. (at^2, 2at) — The standard parametric coordinates for y^2 = 4ax are (at^2, 2at).

Q: A parabola has focus at (3, 0) and directrix x = -3. Its equation is:

Answer: A. y^2 = 12x — The vertex is midway between the focus and directrix, so a = 3. Hence the equation is y^2 = 4ax = 12x.

Q: A tangent to the parabola y^2 = 4ax is parallel to the line y = mx + c. Then the tangent can be represented by:

Answer: A. y = mx + a/m — For y^2 = 4ax, a tangent with slope m has equation y = mx + a/m, obtained from the standard tangent form.

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

Practice Unit 3: Parabola 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 equations of parabola focal distance directrix axis vertex parametric coordinates equations of tangent normal and geometric properties.. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Unit 3: Parabola — Important Questions & Answers (FAQ)

Frequently asked questions from Telangana State Board CLASS 12 INTERMEDIATE 2 YEAR MATHEMATICS - 2B — Unit 3: Parabola, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the standard equation of a parabola with vertex at the origin and axis along the positive x-axis?

A. y^2 = 4ax ✓
B. x^2 = 4ay
C. y^2 = -4ax
D. x^2 = -4ay

Answer: A. y^2 = 4ax
For a parabola opening to the right with vertex at the origin, the standard form is y^2 = 4ax.

In the parabola y^2 = 4ax, the focus is at:

A. (a, 0) ✓
B. (0, a)
C. (-a, 0)
D. (0, -a)

Answer: A. (a, 0)
The parabola y^2 = 4ax has focus at (a, 0) and directrix x = -a.

If a point P lies on the parabola y^2 = 4ax with parametric coordinate t, then P is:

A. (at^2, 2at) ✓
B. (2at, at^2)
C. (a/t^2, 2a/t)
D. (t^2, 4at)

Answer: A. (at^2, 2at)
The standard parametric coordinates for y^2 = 4ax are (at^2, 2at).

A parabola has focus at (3, 0) and directrix x = -3. Its equation is:

A. y^2 = 12x ✓
B. x^2 = 12y
C. y^2 = -12x
D. x^2 = -12y

Answer: A. y^2 = 12x
The vertex is midway between the focus and directrix, so a = 3. Hence the equation is y^2 = 4ax = 12x.

A tangent to the parabola y^2 = 4ax is parallel to the line y = mx + c. Then the tangent can be represented by:

A. y = mx + a/m ✓
B. y = mx - a/m
C. y = -mx + a/m
D. y = x/m + a

Answer: A. y = mx + a/m
For y^2 = 4ax, a tangent with slope m has equation y = mx + a/m, obtained from the standard tangent form.

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