If (4, p) and (1, 0) are end points of the diameter of a circle of length 10cm. fine the centre of the circle.
Answers
Given : (4, p) and (1, 0) are end points of the diameter of a circle of
length 10cm
To Find : centre of the circle
Solution:
(4, p) and (1, 0) are end points of the diameter of a circle
=> 10² = (4 - 1)² + (p - 0)²
=> 100 = 9 + p²
=> p² = 91
=> p = ±√91
Case 1 :
p = +√91
(4, √91) and (1, 0)
Center of circle will be mid point
= ( 5/2 , √91/2)
Case 2 :
p =-√91
(4, -√91) and (1, 0)
Center of circle will be mid point
= ( 5/2 , -√91/2)
Center of circle is ( 5/2 , ±√91/2)
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Answer:
Given : (4, p) and (1, 0) are end points of the diameter of a circle of length 10cm
To Find : centre of the circle
Solution:
(4, p) and (1, 0) are end points of the diameter of a circle
=> 102 = (4 - 1)2 + (p - 0)2 => 100 = 9+p?
=> p² = 91
=> p = ±✓91
Case 1:
p = +✓91
(4, ✓91) and (1, 0)
Center of circle will be mid point
( 5/2 , √91/2)
Case 2:
p = -✓91
(4, -✓91) and (1, O)
Center of circle will be mid point
= ( 5/2 , -✓91/2).
SO THE COORDINATES OF THE CENTER OF THE CIRCLE CAN BE ( 5/2 , √91/2) AND ( 5/2 , -✓91).