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Conic Sections Practice Questions

Class 11 · Mathematics · 850 free MCQs with instant results and detailed explanations.

850
Total
337
Easy
374
Medium
139
Hard

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Topics in Conic Sections

Parabola 246
Circle 264
Ellipse 178
Hyperbola 162

Sample Questions from Conic Sections

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the standard form of the equation of a circle with center at (3, 4) and radius 5?
A. (x - 3)² + (y - 4)² = 25
B. (x + 3)² + (y + 4)² = 25
C. (x - 3)² + (y + 4)² = 25
D. (x + 3)² + (y - 4)² = 25
Show Answer & Explanation
Correct Answer: A
The standard form is (x - h)² + (y - k)² = r², where (h,k) is the center and r is the radius.
Q2
Easy
What is the radius of the circle represented by the equation (x - 1)² + (y + 2)² = 16?
A. 4
B. 3
C. 5
D. 6
Show Answer & Explanation
Correct Answer: A
The radius is found by taking the square root of the right side of the equation.
Q3
Easy
If a circle has an equation of the form (x - 2)² + (y + 3)² = r², what is the y-coordinate of the center?
A. 3
B. -3
C. 2
D. -2
Show Answer & Explanation
Correct Answer: B
The y-coordinate of the center is given by the opposite sign of the constant in the equation.
Q4
Medium
What is the equation of a circle with center at (3, -2) and radius 5?
A. (x - 3)² + (y + 2)² = 25
B. (x + 3)² + (y - 2)² = 25
C. (x - 3)² + (y - 2)² = 5
D. (x + 3)² + (y + 2)² = 5
Show Answer & Explanation
Correct Answer: A
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Q5
Medium
If a circle passes through points (0,0), (6,0), and (3,4), what is the equation of the circle?
A. (x - 3)² + (y - 4)² = 25
B. (x - 3)² + (y + 4)² = 25
C. x² + y² - 6x + 8y = 0
D. (x - 3)² + (y - 2)² = 25
Show Answer & Explanation
Correct Answer: A
The circle must pass through all three points, and we can derive the equation using the standard form.
Q6
Medium
What is the distance between the center of the circle (1, 2) and the point (4, 6)?
A. 3
B. 5
C. 6
D. 7
Show Answer & Explanation
Correct Answer: B
The distance between two points (x1, y1) and (x2, y2) is given by the distance formula: √((x2 - x1)² + (y2 - y1)²).
Q7
Medium
A circle is tangent to the x-axis at the point (2, 0). What is the center of the circle if its radius is 3?
A. (2, 3)
B. (2, -3)
C. (5, 0)
D. (0, 3)
Show Answer & Explanation
Correct Answer: A
If a circle is tangent to the x-axis, the distance from the center to the x-axis is equal to the radius.
Q8
Hard
A circle is defined by the equation (x - 3)² + (y + 4)² = 25. What are the coordinates of the center of this circle?
A. (3, -4)
B. (3, 4)
C. (-3, -4)
D. (4, 3)
Show Answer & Explanation
Correct Answer: A
The center of the circle (h, k) is given by the form (x - h)² + (y - k)² = r². Here, h = 3 and k = -4.
Q9
Hard
Which of the following equations represents a circle whose center is at the origin and has a radius of 5?
A. x² + y² = 25
B. x² + y² = 5
C. x² - y² = 25
D. 2x² + 2y² = 25
Show Answer & Explanation
Correct Answer: A
The standard form for a circle with center at the origin is x² + y² = r², where r is the radius.
Q10
Hard
If a circle with center (h, k) has a radius r, what is the equation of the circle?
A. (x - h)² + (y - k)² = r²
B. x² + y² = r
C. x² + y² + h + k = r²
D. (x + h)² + (y + k)² = r²
Show Answer & Explanation
Correct Answer: A
The general equation for a circle with center (h, k) and radius r is given by the form (x - h)² + (y - k)² = r².

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Conic Sections — Class 11 Mathematics Practice Questions Online

This page contains 850 practice MCQs for the chapter Conic Sections in Class 11 Mathematics. The questions are organized by difficulty — 337 easy, 374 medium, 139 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 4 topics, giving you comprehensive coverage of the entire chapter.