Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?
Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?
The correct option is A The number of intersection points between PQ and circle changes from
0→1→2→1→0.
Let us figure out the number of intersection points between line PQ and circle at different stages of its movement.
Initially we can see the line does not have any intersection points with circle as it is away from circle. Hence, number of intersection points is 0.
When we continue moving line towards circle we will reach the situation where the circle just touches boundary of circle. This is illustrated below. Now, number of intersection points is 1.
When we now move the line into circle, it is obvious that the line intersects the circle at 2 points. The below diagram illustrates this fact. Now, number of intersection points is 2.
When we keep moving PQ towards right, the line will keep moving towards the right-most boundary of circle. When this happens and it touches the boundary, the number of intersection points is 1. After it leaves boundary again, it will never intersect with circle again and number of intersection points will stay 0 forever.
The number of intersection points between PQ and circle changes from
0→1→2→1→0.
Let us figure out the number of intersection points between line PQ and circle at different stages of its movement.
Initially we can see the line does not have any intersection points with circle as it is away from circle. Hence, number of intersection points is 0.
When we continue moving line towards circle we will reach the situation where the circle just touches boundary of circle. This is illustrated below. Now, number of intersection points is 1.
When we now move the line into circle, it is obvious that the line intersects the circle at 2 points. The below diagram illustrates this fact. Now, number of intersection points is 2.
When we keep moving PQ towards right, the line will keep moving towards the right-most boundary of circle. When this happens and it touches the boundary, the number of intersection points is 1. After it leaves boundary again, it will never intersect with circle again and number of intersection points will stay 0 forever.
