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Coordinate Geometry: Circles Practice Questions

JEE · Mathematics · 1781 free MCQs with instant results and detailed explanations.

1781
Total
387
Easy
786
Medium
608
Hard

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Topics in Coordinate Geometry: Circles

Family of Circles 204
Tangent and Normal 357
Standard Equation 265
Chord of Contact 329
General Equation 248
Radical Axis 378

Sample Questions from Coordinate Geometry: Circles

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

Q1
Easy
A circle has a center at (0, 0) and passes through the point (4, 3). What is the radius of the circle?
A. 5
B. 7
C. 3
D. 4
Show Answer & Explanation
Correct Answer: A
The radius is the distance from the center to the point on the circle, calculated using the distance formula.
Q2
Easy
Which equation represents a circle with radius 10 centered at (-5, 7)?
A. (x + 5)² + (y - 7)² = 100
B. (x - 5)² + (y + 7)² = 10
C. (x + 5)² + (y + 7)² = 100
D. (x - 5)² + (y - 7)² = 100
Show Answer & Explanation
Correct Answer: A
The formula for the standard equation of a circle is (x-h)² + (y-k)² = r² with center (h, k) and radius r.
Q3
Easy
A circle is defined by the equation (x + 1)² + (y - 3)² = 49. What is the radius of this circle?
A. 7
B. 14
C. 3
D. 5
Show Answer & Explanation
Correct Answer: A
The radius can be calculated as the square root of the number on the right side of the equation.
Q4
Medium
What is the standard 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 + 2)² + (y - 3)² = 25
Show Answer & Explanation
Correct Answer: A
The standard form of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.
Q5
Medium
Which of the following is the equation of a circle centered at (-2, 5) with a radius of 4?
A. (x + 2)² + (y - 5)² = 16
B. (x - 2)² + (y + 5)² = 16
C. (x - 2)² + (y - 5)² = 16
D. (x + 2)² + (y + 5)² = 16
Show Answer & Explanation
Correct Answer: A
Substituting the center and radius into the standard circle equation gives the correct form.
Q6
Medium
What is the radius of the circle defined by the equation (x - 1)² + (y + 3)² = 49?
A. 7
B. 6
C. 5
D. 8
Show Answer & Explanation
Correct Answer: A
The radius is the square root of the constant on the right side of the equation.
Q7
Medium
What is the standard equation of a circle with center at the origin and radius 10?
A. x² + y² = 100
B. x² + y² = 10
C. x² + y² = 25
D. x² + y² = 50
Show Answer & Explanation
Correct Answer: A
The radius is squared in the equation, yielding the standard form for a circle with center at the origin.
Q8
Hard
If a circle has a radius of √3 and is tangent to the line 2x + 3y - 5 = 0, what is the distance from the center to the line?
A. 1
B. √3
C. 3
D. 2
Show Answer & Explanation
Correct Answer: B
The distance from the center of the circle to the tangent line equals the radius. Here, the radius is √3.
Q9
Hard
A circle intersects the x-axis at points A(2, 0) and B(6, 0). Find the length of the chord AB.
A. 4
B. 8
C. 2
D. 6
Show Answer & Explanation
Correct Answer: A
The length of the chord AB on x-axis can be calculated using the distance formula between points A and B.
Q10
Hard
A circle has its center at (0, 0) and passes through (3, 4). What is the radius of the circle?
A. 7
B. 5
C. 4
D. 3
Show Answer & Explanation
Correct Answer: B
Using the distance formula, the radius is calculated as r = √[(3 - 0)² + (4 - 0)²] = √25 = 5.

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Coordinate Geometry: Circles — JEE Mathematics Practice Questions Online

This page contains 1781 practice MCQs for the chapter Coordinate Geometry: Circles in JEE Mathematics. The questions are organized by difficulty — 387 easy, 786 medium, 608 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 6 topics, giving you comprehensive coverage of the entire chapter.