Coordinate Geometry MCQ & Objective Questions
Coordinate Geometry is a crucial topic for students preparing for school exams and competitive tests in India. Mastering this subject not only enhances your understanding of geometric concepts but also significantly boosts your performance in exams. Practicing MCQs and objective questions on Coordinate Geometry helps you identify important questions and strengthens your exam preparation strategy.
What You Will Practise Here
Understanding the Cartesian coordinate system and plotting points.
Finding the distance between two points using the distance formula.
Determining the midpoint of a line segment.
Exploring the slope of a line and its significance.
Analyzing equations of lines, including slope-intercept and point-slope forms.
Working with the equations of circles and their properties.
Solving problems involving the area of triangles and quadrilaterals in the coordinate plane.
Exam Relevance
Coordinate Geometry is a vital part of the curriculum for CBSE, State Boards, NEET, and JEE exams. Questions from this topic often appear in various formats, including direct application problems, conceptual understanding, and graphical interpretations. Students can expect to encounter questions that require them to apply formulas, interpret graphs, and solve real-world problems, making it essential to practice thoroughly.
Common Mistakes Students Make
Confusing the formulas for distance and midpoint, leading to calculation errors.
Misinterpreting the slope of a line, especially when dealing with vertical and horizontal lines.
Overlooking the significance of signs in coordinate points, which can alter the outcome of problems.
Failing to convert between different forms of line equations when required.
FAQs
Question: What are the key formulas I need to remember for Coordinate Geometry?Answer: The key formulas include the distance formula, midpoint formula, and the slope formula, which are essential for solving problems in this topic.
Question: How can I improve my speed in solving Coordinate Geometry MCQs?Answer: Regular practice with timed quizzes and focusing on understanding concepts rather than rote memorization can help improve your speed and accuracy.
Start solving practice MCQs on Coordinate Geometry today to test your understanding and enhance your exam readiness. Remember, consistent practice is the key to mastering this topic and achieving your academic goals!
Q. A circle is defined by the equation x² + y² - 10x + 6y + 25 = 0. What is the radius of the circle?
Show solution
Solution
Rearranging gives (x - 5)² + (y + 3)² = 9, so the radius is √9 = 3.
Correct Answer:
A
— 5
Learn More →
Q. A circle is inscribed in a triangle with sides 7, 8, and 9. What is the radius of the circle?
Show solution
Solution
Using the formula for the radius of the incircle r = A/s, where A is the area and s is the semi-perimeter.
Correct Answer:
B
— 5
Learn More →
Q. A circle is inscribed in a triangle with sides 7, 8, and 9. What is the radius of the inscribed circle?
Show solution
Solution
Using the formula for the radius of the incircle r = A/s, where A is the area and s is the semi-perimeter.
Correct Answer:
B
— 4
Learn More →
Q. A circle is tangent to the x-axis at the point (4, 0). What is the equation of the circle if its radius is 3?
A.
(x - 4)² + (y - 3)² = 9
B.
(x - 4)² + (y + 3)² = 9
C.
(x + 4)² + (y - 3)² = 9
D.
(x + 4)² + (y + 3)² = 9
Show solution
Solution
The center of the circle is (4, 3) since it is 3 units above the tangent point (4, 0).
Correct Answer:
B
— (x - 4)² + (y + 3)² = 9
Learn More →
Q. A circle passes through the points (1, 2), (3, 4), and (5, 6). What is the radius of the circle?
Show solution
Solution
Using the distance formula, the radius can be calculated from the center found using the circumcircle method.
Correct Answer:
B
— 3
Learn More →
Q. Determine the area of the triangle formed by the points (0, 0), (4, 0), and (0, 3).
Show solution
Solution
Area = 1/2 * base * height = 1/2 * 4 * 3 = 6.
Correct Answer:
A
— 6
Learn More →
Q. Determine the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be perpendicular.
A.
h^2 = ab
B.
h^2 = -ab
C.
a + b = 0
D.
a - b = 0
Show solution
Solution
The lines are perpendicular if 2h = a + b, which leads to h^2 = -ab.
Correct Answer:
B
— h^2 = -ab
Learn More →
Q. Determine the condition for the lines represented by ax^2 + 2hxy + by^2 = 0 to be parallel.
A.
h^2 = ab
B.
h^2 > ab
C.
h^2 < ab
D.
h^2 ≠ ab
Show solution
Solution
The lines are parallel if the discriminant of the quadratic equation is zero, which leads to the condition h^2 = ab.
Correct Answer:
A
— h^2 = ab
Learn More →
Q. Determine the condition for the lines represented by the equation 4x^2 + 4xy + y^2 = 0 to be coincident.
A.
b^2 - 4ac = 0
B.
b^2 - 4ac > 0
C.
b^2 - 4ac < 0
D.
b^2 - 4ac = 1
Show solution
Solution
For the lines to be coincident, the discriminant must be zero, i.e., b^2 - 4ac = 0.
Correct Answer:
A
— b^2 - 4ac = 0
Learn More →
Q. Determine the condition for the lines represented by the equation ax^2 + 2hxy + by^2 = 0 to be perpendicular.
A.
a + b = 0
B.
ab = h^2
C.
a - b = 0
D.
h = 0
Show solution
Solution
The lines are perpendicular if the condition a + b = 0 holds true.
Correct Answer:
A
— a + b = 0
Learn More →
Q. Determine the coordinates of the centroid of the triangle with vertices at (0, 0), (6, 0), and (3, 6).
A.
(3, 2)
B.
(3, 3)
C.
(2, 3)
D.
(0, 0)
Show solution
Solution
Centroid = ((0+6+3)/3, (0+0+6)/3) = (3, 2).
Correct Answer:
B
— (3, 3)
Learn More →
Q. Determine the equation of the circle with center (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
Equation of circle: (x - h)² + (y - k)² = r² => (x - 2)² + (y + 3)² = 5² = 25.
Correct Answer:
A
— (x - 2)² + (y + 3)² = 25
Learn More →
Q. Determine the equation of the line that passes through the points (0, 0) and (3, 9).
A.
y = 3x
B.
y = 2x
C.
y = 3x + 1
D.
y = x + 1
Show solution
Solution
The slope m = (9 - 0) / (3 - 0) = 3. The equation is y = 3x.
Correct Answer:
A
— y = 3x
Learn More →
Q. Determine the family of curves represented by the equation x^2 - y^2 = c, where c is a constant.
A.
Circles
B.
Ellipses
C.
Hyperbolas
D.
Parabolas
Show solution
Solution
The equation x^2 - y^2 = c represents a family of hyperbolas with varying values of c.
Correct Answer:
C
— Hyperbolas
Learn More →
Q. Determine the family of curves represented by the equation x^2/a^2 + y^2/b^2 = 1.
A.
Circles
B.
Ellipses with varying axes
C.
Hyperbolas
D.
Parabolas
Show solution
Solution
The equation x^2/a^2 + y^2/b^2 = 1 represents a family of ellipses with varying semi-major and semi-minor axes.
Correct Answer:
B
— Ellipses with varying axes
Learn More →
Q. Determine the family of curves represented by the equation y = ax^2 + bx + c.
A.
Parabolas
B.
Circles
C.
Ellipses
D.
Straight lines
Show solution
Solution
The equation y = ax^2 + bx + c represents a family of parabolas with varying coefficients a, b, and c.
Correct Answer:
A
— Parabolas
Learn More →
Q. Determine the family of curves represented by the equation y = ax^3 + bx.
A.
Cubic functions
B.
Quadratic functions
C.
Linear functions
D.
Exponential functions
Show solution
Solution
The equation y = ax^3 + bx represents a family of cubic functions where a and b are constants.
Correct Answer:
A
— Cubic functions
Learn More →
Q. Determine the family of curves represented by the equation y = ax^3 + bx^2 + cx + d.
A.
Cubic functions
B.
Quadratic functions
C.
Linear functions
D.
Exponential functions
Show solution
Solution
The equation y = ax^3 + bx^2 + cx + d represents a family of cubic functions.
Correct Answer:
A
— Cubic functions
Learn More →
Q. Determine the family of curves represented by the equation y = e^(kx) for varying k.
A.
Exponential curves
B.
Linear functions
C.
Quadratic functions
D.
Logarithmic functions
Show solution
Solution
The equation y = e^(kx) represents a family of exponential curves with varying growth rates determined by k.
Correct Answer:
A
— Exponential curves
Learn More →
Q. Determine the family of curves represented by the equation y = k/x, where k is a constant.
A.
Hyperbolas
B.
Circles
C.
Ellipses
D.
Parabolas
Show solution
Solution
The equation y = k/x represents a family of hyperbolas with varying values of 'k'.
Correct Answer:
A
— Hyperbolas
Learn More →
Q. Determine the family of curves represented by the equation y = kx^2, where k is a constant.
A.
Circles
B.
Ellipses
C.
Parabolas
D.
Hyperbolas
Show solution
Solution
The equation y = kx^2 represents a family of parabolas that open upwards or downwards depending on the sign of k.
Correct Answer:
C
— Parabolas
Learn More →
Q. Determine the focus of the parabola defined by the equation x^2 = 12y.
A.
(0, 3)
B.
(0, -3)
C.
(3, 0)
D.
(-3, 0)
Show solution
Solution
The equation x^2 = 4py gives 4p = 12, hence p = 3. The focus is at (0, p) = (0, 3).
Correct Answer:
A
— (0, 3)
Learn More →
Q. Determine the focus of the parabola given by the equation x^2 = 8y.
A.
(0, 2)
B.
(0, 4)
C.
(2, 0)
D.
(4, 0)
Show solution
Solution
The standard form of the parabola is x^2 = 4py. Here, 4p = 8, so p = 2. The focus is at (0, p) = (0, 2).
Correct Answer:
B
— (0, 4)
Learn More →
Q. Determine the length of the latus rectum of the parabola y^2 = 16x.
Show solution
Solution
The length of the latus rectum for the parabola y^2 = 4px is given by 4p. Here, p = 4, so the length is 16.
Correct Answer:
B
— 8
Learn More →
Q. Determine the nature of the lines represented by the equation 7x^2 + 2xy + 3y^2 = 0.
A.
Parallel
B.
Intersecting
C.
Coincident
D.
Perpendicular
Show solution
Solution
The discriminant indicates that the lines intersect at two distinct points.
Correct Answer:
B
— Intersecting
Learn More →
Q. Determine the point of intersection of the lines y = 2x + 1 and y = -x + 4.
A.
(1, 3)
B.
(2, 5)
C.
(3, 7)
D.
(4, 9)
Show solution
Solution
Setting 2x + 1 = -x + 4 gives 3x = 3, hence x = 1. Substituting back gives y = 3.
Correct Answer:
A
— (1, 3)
Learn More →
Q. Determine the x-intercept of the line 4x - 2y + 8 = 0.
Show solution
Solution
Setting y = 0 in the equation gives 4x + 8 = 0, thus x = -2.
Correct Answer:
B
— 2
Learn More →
Q. Determine the x-intercept of the line 4x - 5y + 20 = 0.
Show solution
Solution
Setting y = 0 in the equation gives 4x + 20 = 0, thus x = -5.
Correct Answer:
D
— -4
Learn More →
Q. Determine the x-intercept of the line 5x + 2y - 10 = 0.
Show solution
Solution
Setting y = 0 in the equation gives 5x - 10 = 0, thus x = 2.
Correct Answer:
B
— 5
Learn More →
Q. Determine the x-intercept of the line given by the equation 2x - 3y + 6 = 0.
Show solution
Solution
Set y = 0 in the equation: 2x + 6 = 0 => x = -3.
Correct Answer:
B
— 3
Learn More →
Showing 1 to 30 of 361 (13 Pages)
