Q. Diameter of a circle which passes through (-2,3) is 10 units . If the center of the circle is
(3x-1,5x+1) , find x .
D = 10 units .
R = 5 units .
Now :-
By distance formula :-
___________________________
d = √ ( 3x - 1 + 2 )2 + ( 5x + 1 - 3 )2 = 5
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√ ( 3x + 1 )2 + ( 5x - 2 )2 = 5
Squaring on both sides :-
9x2 + 1 + 6x + 25x2 + 4 - 20x = 25
34x2 - 14x + 5 - 25 = 0
34x2 - 14x - 20 = 0
Dividing equation by 2 :-
17x2 - 7x - 10 = 0
17x2 - 17x + 10x - 10 = 0
17x ( x - 1 ) + 10 ( x - 1 ) = 0
( 17x + 10 ) ( x - 1 ) = 0
x = - 10 / 17 or 1
- 10 / 17 is denied
x = 1
Hope it helps ..!!
R = 5 units .
Now :-
By distance formula :-
___________________________
d = √ ( 3x - 1 + 2 )2 + ( 5x + 1 - 3 )2 = 5
__________________
√ ( 3x + 1 )2 + ( 5x - 2 )2 = 5
Squaring on both sides :-
9x2 + 1 + 6x + 25x2 + 4 - 20x = 25
34x2 - 14x + 5 - 25 = 0
34x2 - 14x - 20 = 0
Dividing equation by 2 :-
17x2 - 7x - 10 = 0
17x2 - 17x + 10x - 10 = 0
17x ( x - 1 ) + 10 ( x - 1 ) = 0
( 17x + 10 ) ( x - 1 ) = 0
x = - 10 / 17 or 1
- 10 / 17 is denied
x = 1
Hope it helps ..!!