Q. What is the angle between the lines represented by the equations y = 2x + 1 and y = -1/2x + 3? (2021)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 2 and m2 = -1/2. The angle θ between the lines is given by tan(θ) = |(m1 - m2) / (1 + m1*m2)|, which results in 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. What is the angle between the lines y = 3x + 2 and y = -1/3x + 1? (2021)
A.
90 degrees
B.
45 degrees
C.
60 degrees
D.
30 degrees
Show solution
Solution
The slopes are m1 = 3 and m2 = -1/3. The angle θ = tan⁻¹(|(m1 - m2) / (1 + m1*m2)|) = tan⁻¹(10/8) = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. What is the axis of symmetry for the parabola given by the equation y = -3(x - 2)^2 + 5?
A.
x = 2
B.
y = 5
C.
y = -3
D.
x = -2
Show solution
Solution
The axis of symmetry for a parabola in vertex form y = a(x - h)^2 + k is x = h. Here, h = 2.
Correct Answer:
A
— x = 2
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Q. What is the axis of symmetry for the parabola given by the equation y^2 = 6x?
A.
x-axis
B.
y-axis
C.
y = x
D.
x = 0
Show solution
Solution
The axis of symmetry for the parabola y^2 = 4px is the x-axis.
Correct Answer:
B
— y-axis
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Q. What is the directrix of the parabola defined by the equation y^2 = 20x?
A.
x = -5
B.
x = 5
C.
y = 5
D.
y = -5
Show solution
Solution
For the equation y^2 = 4px, p = 5. The directrix is given by x = -p, which is x = -5.
Correct Answer:
A
— x = -5
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Q. What is the distance between the points (0, 0) and (3, 4)?
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Solution
Using the distance formula: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the points (0, 0) and (8, 6)?
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Solution
Using the distance formula: d = √((8 - 0)² + (6 - 0)²) = √(64 + 36) = √100 = 10.
Correct Answer:
A
— 10
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Q. What is the distance between the points (0, 0) and (x, y) where x = 3 and y = 4? (2022)
Show solution
Solution
Using the distance formula: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the distance between the points (2, 3) and (6, 7)?
Show solution
Solution
Using the distance formula: d = √[(6 - 2)² + (7 - 3)²] = √[16 + 16] = √32 = 4√2 ≈ 5.66.
Correct Answer:
A
— 5
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Q. What is the distance between the points (3, 2) and (3, -2)?
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Solution
Using the distance formula: d = √[(3 - 3)² + (-2 - 2)²] = √[0 + 16] = √16 = 4.
Correct Answer:
A
— 4
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Q. What is the distance between the points (3, 7) and (3, 1)?
Show solution
Solution
Using the distance formula: d = √[(3 - 3)² + (1 - 7)²] = √[0 + 36] = √36 = 6.
Correct Answer:
A
— 6
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Q. What is the distance between the points (5, 5) and (1, 1)?
Show solution
Solution
Using the distance formula: d = √[(1 - 5)² + (1 - 5)²] = √[16 + 16] = √32 = 4√2.
Correct Answer:
A
— 4√2
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Q. What is the distance between the points (6, 8) and (6, 2)?
Show solution
Solution
Using the distance formula: d = √[(6 - 6)² + (2 - 8)²] = √[0 + 36] = √36 = 6.
Correct Answer:
A
— 6
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Q. What is the equation of the circle with center at (2, -3) and radius 5?
A.
(x-2)² + (y+3)² = 25
B.
(x+2)² + (y-3)² = 25
C.
(x-2)² + (y-3)² = 25
D.
(x+2)² + (y+3)² = 25
Show solution
Solution
Standard form of a circle: (x-h)² + (y-k)² = r². Here, h=2, k=-3, r=5.
Correct Answer:
A
— (x-2)² + (y+3)² = 25
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Q. What is the equation of the directrix of the parabola x^2 = 12y?
A.
y = 3
B.
y = -3
C.
y = 6
D.
y = -6
Show solution
Solution
The directrix of the parabola x^2 = 4py is given by y = -p. Here, p = 3, so the directrix is y = -3.
Correct Answer:
B
— y = -3
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Q. What is the equation of the line parallel to y = 3x + 2 that passes through the point (4, 1)? (2020)
A.
y = 3x - 11
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x - 2
Show solution
Solution
Since parallel lines have the same slope, the equation is y - 1 = 3(x - 4) which simplifies to y = 3x - 11.
Correct Answer:
A
— y = 3x - 11
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Q. What is the equation of the line parallel to y = 3x + 4 that passes through the point (1, 2)? (2020)
A.
y = 3x - 1
B.
y = 3x + 1
C.
y = 3x + 2
D.
y = 3x - 2
Show solution
Solution
Parallel lines have the same slope. Using point-slope form: y - 2 = 3(x - 1) gives y = 3x - 1.
Correct Answer:
A
— y = 3x - 1
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Q. What is the equation of the line parallel to y = 3x - 4 that passes through the point (2, 1)? (2020)
A.
y = 3x - 5
B.
y = 3x + 1
C.
y = 3x - 1
D.
y = 3x + 4
Show solution
Solution
Since parallel lines have the same slope, the equation is y - 1 = 3(x - 2) which simplifies to y = 3x - 5.
Correct Answer:
C
— y = 3x - 1
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Q. What is the equation of the line that is perpendicular to y = 3x + 2 and passes through the point (1, 1)? (2022)
A.
y = -1/3x + 4/3
B.
y = 3x - 2
C.
y = -3x + 4
D.
y = 1/3x + 2/3
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1) gives y = -1/3x + 4/3.
Correct Answer:
A
— y = -1/3x + 4/3
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Q. What is the equation of the line that is perpendicular to y = 3x + 4 and passes through the point (1, 1)? (2022)
A.
y - 1 = -1/3(x - 1)
B.
y - 1 = 3(x - 1)
C.
y - 1 = 3/1(x - 1)
D.
y - 1 = -3(x - 1)
Show solution
Solution
The slope of the perpendicular line is -1/3. Using point-slope form: y - 1 = -1/3(x - 1).
Correct Answer:
A
— y - 1 = -1/3(x - 1)
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Q. What is the equation of the line that passes through the origin and has a slope of -4? (2023)
A.
y = -4x
B.
y = 4x
C.
y = -x/4
D.
y = 1/4x
Show solution
Solution
Using the slope-intercept form y = mx + b, with m = -4 and b = 0, the equation is y = -4x.
Correct Answer:
A
— y = -4x
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Q. What is the equation of the line that passes through the origin and has a slope of -3? (2022)
A.
y = -3x
B.
y = 3x
C.
y = -x/3
D.
y = 1/3x
Show solution
Solution
The equation of a line through the origin with slope m is y = mx. Thus, y = -3x.
Correct Answer:
A
— y = -3x
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Q. What is the focus of the parabola defined by the equation y^2 = 20x?
A.
(5, 0)
B.
(0, 5)
C.
(0, 10)
D.
(10, 0)
Show solution
Solution
In the equation y^2 = 4px, we have 4p = 20, thus p = 5. The focus is at (5, 0).
Correct Answer:
A
— (5, 0)
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Q. What is the focus of the parabola given by the equation y^2 = 20x?
A.
(5, 0)
B.
(0, 5)
C.
(0, -5)
D.
(10, 0)
Show solution
Solution
For the parabola y^2 = 4px, here 4p = 20, so p = 5. The focus is at (5, 0).
Correct Answer:
A
— (5, 0)
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Q. What is the latus rectum of the parabola given by the equation y^2 = 12x?
Show solution
Solution
The latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 12, so p = 3, and the latus rectum is 4p = 12.
Correct Answer:
C
— 6
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Q. What is the length of the line segment between the points (3, 4) and (7, 1)? (2023)
Show solution
Solution
Using the distance formula, length = sqrt((7-3)^2 + (1-4)^2) = sqrt(16 + 9) = 5.
Correct Answer:
A
— 5
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Q. What is the slope of the line perpendicular to the line 4x - 5y + 10 = 0? (2022)
A.
5/4
B.
-4/5
C.
4/5
D.
-5/4
Show solution
Solution
The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.
Correct Answer:
B
— -4/5
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Q. What is the slope of the line perpendicular to the line 4x - 5y = 10? (2022)
A.
5/4
B.
-4/5
C.
4/5
D.
-5/4
Show solution
Solution
The slope of the line is 4/5, so the slope of the perpendicular line is -5/4.
Correct Answer:
B
— -4/5
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Q. What is the slope of the line represented by the equation 4x - 2y + 8 = 0? (2021)
Show solution
Solution
Rearranging gives y = 2x + 4, so slope = 2.
Correct Answer:
C
— -2
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Q. What is the value of p for the parabola defined by the equation y^2 = 20x?
Show solution
Solution
In the equation y^2 = 4px, we have 4p = 20, thus p = 5.
Correct Answer:
A
— 5
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Showing 61 to 90 of 99 (4 Pages)
Coordinate Geometry MCQ & Objective Questions
Coordinate Geometry is a crucial topic for students preparing for school and competitive exams in India. Mastering this subject not only enhances your understanding of geometric concepts but also significantly boosts your exam scores. Practicing MCQs and objective questions helps in reinforcing your knowledge and identifying important questions that frequently appear in exams.
What You Will Practise Here
Understanding the Cartesian coordinate system and plotting points.
Key formulas for distance, midpoint, and section formula.
Equations of lines: slope-intercept form, point-slope form, and standard form.
Concepts of parallel and perpendicular lines in the coordinate plane.
Finding the area of triangles and other polygons using coordinates.
Applications of coordinate geometry in real-life problems.
Graphical representation of linear equations and inequalities.
Exam Relevance
Coordinate Geometry is a vital part of the mathematics syllabus for CBSE, State Boards, NEET, and JEE. Questions from this topic often include finding distances, determining slopes, and solving equations of lines. Students can expect to encounter both direct application questions and conceptual problems that test their understanding of the subject. Familiarity with common question patterns will aid in effective exam preparation.
Common Mistakes Students Make
Confusing the different forms of linear equations.
Miscalculating distances or midpoints due to sign errors.
Overlooking the significance of slopes in determining line relationships.
Failing to apply the correct formula in area calculations.
FAQs
Question: What is the importance of practicing Coordinate Geometry MCQ questions?Answer: Practicing MCQ questions helps reinforce concepts, improves problem-solving speed, and boosts confidence for exams.
Question: How can I effectively prepare for Coordinate Geometry objective questions with answers?Answer: Regular practice of important Coordinate Geometry questions for exams and reviewing mistakes can enhance your understanding and retention.
Start solving practice MCQs today to test your understanding and excel in your exams. Remember, consistent practice is the key to mastering Coordinate Geometry!
