Quiz for Circles

Q1: What is the general equation of a circle?

A. x² + y² = r² B. (x - a)² + (y - b)² = r² C. x² + y² + 2gx + 2fy + c = 0 D. None of these

Q2: What is the center of the circle x² + y² + 6x - 8y + 9 = 0?

A. (-3, 4) B. (3, -4) C. (6, 8) D. (-6, 8)

Q3: If the radius of a circle is 5, what is the length of its diameter?

A. 5 B. 10 C. 25 D. 2.5

Q4: A circle passes through (0,0) and has center (3,4). What is its radius?

A. 3 B. 4 C. 5 D. 7

Q5: What is the condition for two circles to be orthogonal?

A. Sum of radii = 0 B. Product of slopes = -1 C. Angle between tangents = 90° D. 2g₁g₂ + 2f₁f₂ = c₁ + c₂

Q6: Which point lies on the circle x² + y² = 25?

A. (3, 4) B. (5, 5) C. (6, 0) D. (0, 0)

Q7: What is the equation of a circle with center (2, -1) and radius 3?

A. (x + 2)² + (y + 1)² = 9 B. (x - 2)² + (y + 1)² = 9 C. (x - 2)² + (y + 1)² = 3 D. (x - 2)² + (y + 1)² = 6

Q8: Length of tangent from (6, 8) to the circle x² + y² = 25 is:

A. 10 B. 11 C. 5 D. √39

Q9: The maximum number of common tangents between two non-intersecting circles is:

A. 1 B. 2 C. 3 D. 4

Q10: If two circles intersect in two points, then the number of common tangents is:

A. 2 B. 3 C. 4 D. 1

Q11: What is the radical axis of two circles?

A. Line joining centers B. Line perpendicular to centers C. Locus of points with equal power w.r.t both circles D. None of these

Q12: For the circle (x - 1)² + (y + 2)² = 16, what is the radius?

A. 1 B. 2 C. 3 D. 4

Q13: What is the area of a circle with diameter 6?

A. 9π B. 18π C. 36π D. 12π

Q14: The chord passing through the center of a circle is called:

A. Secant B. Radius C. Tangent D. Diameter

Q15: What is the equation of the circle with diameter endpoints (2,3) and (4,7)?

A. (x - 3)² + (y - 5)² = 5 B. (x - 3)² + (y - 5)² = 10 C. (x - 3)² + (y - 5)² = 8 D. (x - 3)² + (y - 5)² = 9

Q16: How many points can a circle and a line intersect at most?

A. 1 B. 2 C. 3 D. Infinite

Q17: If a tangent is drawn from (0,5) to the circle x² + y² = 9, its length is:

A. 5 B. 4 C. √16 D. √25

Q18: Which of the following is always true for a tangent to a circle?

A. It passes through the center B. It is perpendicular to the radius at point of contact C. It is parallel to a chord D. None of these

Q19: What is the locus of a point equidistant from a fixed point and a fixed line?

A. Circle B. Ellipse C. Parabola D. Hyperbola

Q20: A circle with center (h, k) passes through origin. Its radius is:

A. √(h² + k²) B. h + k C. h² + k² D. None