Unit 3: Parabola — Online MCQ Test
MATHEMATICS - 2B · CLASS 12 INTERMEDIATE 2 YEAR · Telangana State Board
Practice Unit 3: Parabola with a free chapter-wise online MCQ test.
This chapter covers: This chapter covers standard equations of parabola focal distance directrix axis vertex parametric coordinates equations of tangent normal and geometric properties..
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Unit 3: Parabola — Important Questions & Answers
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.
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.
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).
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.
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.
For y^2 = 4ax, a tangent with slope m has equation y = mx + a/m, obtained from the standard tangent form.