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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
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GPA: 3.39
In the rectangular coordinate system, points (4, 0) and (– 4, 0) both
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17 Nov 2021, 03:17
17 Nov 2021, 03:17
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71% (00:51) wrong based on 7 sessions
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In the rectangular coordinate system, points (4, 0) and (– 4, 0) both lie on circle C. What is the maximum possible value of the radius of C ?
(A) 2
(B) 4
(C) 8
(D) 16
(E) None of the above
(A) 2
(B) 4
(C) 8
(D) 16
(E) None of the above
Re: In the rectangular coordinate system, points (4, 0) and (– 4, 0) both
[#permalink]
17 Nov 2021, 09:10
17 Nov 2021, 09:10
1
Simply said, radius \(r\) can go to \(\infty\).
\((4,0)\) and \((-4,0)\) lie of the a circle, which means the circle is symmetric about y-axis
Let \((h,k)\) be the center of the circle.
Since the circle is symmetric about y-axis, it makes \(h = 0\)
Equation of this circle -> \((x-h)^2 + (y-k)^2 = r^2\)
Now \((4,0)\) and \((-4,0)\) lie of the a circle.
\((4-0)^2 + (0-k)^2 = r^2\) and \((-4-0)^2 + (0-k)^2 = r^2\)
\((4)^2 + (k)^2 = r^2\)
\(4^2 + k^2 = r^2\)
\(r\) can be interpreted as hypotenuse of a right-angles triangle, considering the Pythagorean Theorem into consideration.
But here is the catch, \(r\) is not restricted to be an integer and hence its value can literally go to infinity.
Hence, Answer is E
\((4,0)\) and \((-4,0)\) lie of the a circle, which means the circle is symmetric about y-axis
Let \((h,k)\) be the center of the circle.
Since the circle is symmetric about y-axis, it makes \(h = 0\)
Equation of this circle -> \((x-h)^2 + (y-k)^2 = r^2\)
Now \((4,0)\) and \((-4,0)\) lie of the a circle.
\((4-0)^2 + (0-k)^2 = r^2\) and \((-4-0)^2 + (0-k)^2 = r^2\)
\((4)^2 + (k)^2 = r^2\)
\(4^2 + k^2 = r^2\)
\(r\) can be interpreted as hypotenuse of a right-angles triangle, considering the Pythagorean Theorem into consideration.
But here is the catch, \(r\) is not restricted to be an integer and hence its value can literally go to infinity.
Hence, Answer is E
gmatclubot
Re: In the rectangular coordinate system, points (4, 0) and (– 4, 0) both [#permalink]
17 Nov 2021, 09:10
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