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प्रश्न
Find the coordinates of a point A, where AB is the diameter of circle whose centre is (2, -3) and B is (1, 4).
Find the coordinates of a point A, where AB is a diameter of a circle with center C (2, -3) and the other end of the diameter is B (1, 4).
उत्तर १
Let the centre of the circle be O.
Since AB is the diameter so, O is the midpoint of AB.
Thus, using the section formula,
`("a" +1)/2 = 2`
⇒ a = 4 - 1
⇒ a = 3
and
`("b" + 4)/2 = -3`
⇒ b = -10
So, the coordinate of point A is (3, -10).
उत्तर २
C (2, -3) is the center of the given circle. Let A(a, b) and B(1, 4) be the two end-points of the given diameter AB. Then, the coordinates of C are
`x = (a+1)/2 , y =( b+4)/2`
It is given that x = 2 and y = -3
⇒ `2= (a+1)/2, 3 = (b+4)/2`
⇒ 4 = a + 1, -6 = b + 4
⇒ a = 4 - 1, b = -6 - 4
⇒ a = 3, b = -10
Therefore, the coordinates of point A are (3, -10).
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