Question

If a line does not intersect any member of circles at two distinct points, where a is a parameter, then the maximum value of a is:

(a) 0

(b) 1

(c) [infinity]

(d) 1/2​

Answer 1

The maximum value of a in the given scenario is 1 (option b). If a line does not intersect any member of circles at two distinct points, it means that the line is a tangent to the circle, touching it at only one point. In this case, the line can be drawn tangent to any circle with a parameter value of a ≤ 1.

Step-by-step explanation:

The maximum value of a in the given scenario is 1 (option b).

If a line does not intersect any member of circles at two distinct points, it means that the line is a tangent to the circle, touching it at only one point. In this case, the line can be drawn tangent to any circle with a parameter value of a ≤ 1.

If the line intersects the circle at two distinct points, it would be a secant, not a tangent.

The question relates to the geometry of circles and their relationship to straight lines. A line that does not intersect a circle at two distinct points is either tangent to the circle at one point or does not touch the circle at all.

For the line to be tangent to the circle, and assuming we are working with a circle inside a square, the maximum value of 'a' would be the radius of that circle which is half the side length of the square.