Final answer:
The length AB, we need to calculate the distance between the points A and B AB is 0.
Step-by-step explanation:
To find the length AB, we need to calculate the distance between the points A and B. The coordinates of point A are (a, √11) and the coordinates of point B are (b, √11). Since the points lie on the circumference of the circle with equation x^2 + y^2 = 36, we can substitute the y-coordinate (√11) into the equation to find the x-coordinates:
a^2 + (√11)^2 = 36
b^2 + (√11)^2 = 36
Simplifying these equations, we get:
a^2 + 11 = 36
b^2 + 11 = 36
Subtracting 11 from both sides:
a^2 = 25
b^2 = 25
Taking the square root of both sides to solve for a and b:
a = ±5
b = ±5
Since we're dealing with points on the circumference, we take the positive values for a and b:
a = 5, b = 5
Now we can calculate the distance between the points using the distance formula:
AB = √((b - a)^2 + (√11 - √11)^2)
AB = √((5 - 5)^2 + (0)^2)
AB = √(0 + 0)
AB = √0
AB = 0
Therefore, the length AB is 0.