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29 May 2018, 22:32
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
77% (02:01) correct
23%
(02:20)
wrong
based on 226
sessions
History
Date
Time
Result
Not Attempted Yet
A circle is centered on point (6,0). If points (−2,0) and (0,x) are on the circle, and x>0, what is the value of x?
A. √28
B. 6
C. √42
D. √84
E. 10
A. √28
B. 6
C. √42
D. √84
E. 10
29 May 2018, 23:06
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Solution
Given:
- • Center of the circle = (6, 0)
• Points on the circle = (-2, 0) and (0, x) where x > 0
To find:
- • The value of x
Approach and Working:
We know that, in any circle the distance between the center and any point which is on the circle is always constant [this is actually the radius of the circle]
Therefore, we can say,
- • Distance between (6, 0) and (0, x) = distance between (6, 0) and (-2, 0)
Or, \(6^2 + x^2 = 8^2 + 0\)
Or, \(x^2 = 64 – 36 = 28\)
Or, x = \(\sqrt{28}\)
Hence, the correct answer is option A.
Answer: A
General Discussion
29 May 2018, 22:54
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A circle is centered on point (6,0). If points (−2,0) and (0,x) are on the circle, and x>0, what is the value of x?
A. √28
B. 6
C. √42
D. √84
E. 10
since, (-2,0) lies on the circle. Therefore r= [{6-(-2)}^2 +(0-0)^2]^1/2 = 64^1/2 = 8.
Also, (0,x) lies on circle that is [{6-0}^2 +(0-x)^2]= 8^2
=> 36+ x^2= 64
=> x^2 = 64-36 = 28
Therefore x = √28
A is the answer.
A. √28
B. 6
C. √42
D. √84
E. 10
since, (-2,0) lies on the circle. Therefore r= [{6-(-2)}^2 +(0-0)^2]^1/2 = 64^1/2 = 8.
Also, (0,x) lies on circle that is [{6-0}^2 +(0-x)^2]= 8^2
=> 36+ x^2= 64
=> x^2 = 64-36 = 28
Therefore x = √28
A is the answer.
