The circle centered at(2,3) and radius 5 units intersects x axis at Aand B find the coordinates of the points A and B also find the lenghth of the chord AB
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Given the center as (2, 3) and the radius as 5 units we can use the formulae of getting the length for line to get the points A and B.
At the point the circle cuts the x axis,
y = 0
Thus we have (x, 0) as the point where the circle cuts the x axis.
Radius = the length of a line that is from any point on the circle to the center of the circle.
CALCULATIONS
R = √(x₁ - x₂) ² + (y₁- y₂ )²
5= √(2 - x) ² + (3 - 0)²
5² = (2 - x) ² + 9
25 - 9 = (2 - x) ²
√16 = 2 - x
4 = 2 - x
x = - 2
Since the lines from these two points A and B are equal and form an isosceles triangle since all lie on the x axis then the x value of the other point will be a positive 2.
Therefore :
A = (-2,0) and B = (2,0)
The length of chord AB is :
√(2+2)² + (0)²= √4² = √16
√16 = 4units
AB = 4units.
At the point the circle cuts the x axis,
y = 0
Thus we have (x, 0) as the point where the circle cuts the x axis.
Radius = the length of a line that is from any point on the circle to the center of the circle.
CALCULATIONS
R = √(x₁ - x₂) ² + (y₁- y₂ )²
5= √(2 - x) ² + (3 - 0)²
5² = (2 - x) ² + 9
25 - 9 = (2 - x) ²
√16 = 2 - x
4 = 2 - x
x = - 2
Since the lines from these two points A and B are equal and form an isosceles triangle since all lie on the x axis then the x value of the other point will be a positive 2.
Therefore :
A = (-2,0) and B = (2,0)
The length of chord AB is :
√(2+2)² + (0)²= √4² = √16
√16 = 4units
AB = 4units.
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