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The center of circle Q is on the y-axis, and the circle passes through

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Magoosh GMAT Instructor
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The center of circle Q is on the y-axis, and the circle passes through  [#permalink]

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New post 26 Nov 2014, 11:48
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  55% (hard)

Question Stats:

67% (01:21) correct 33% (01:41) wrong based on 213 sessions

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The center of circle Q is on the y-axis, and the circle passes through points (0, 7) and (0, –1). Circle Q intersects the positive x-axis at (p, 0). What is the value of p?

(A) \(\frac{7}{3}\)

(B) \(4\)

(C) \(5\)

(D) \(\sqrt{7}\)

(E) \(\sqrt{11}\)


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Re: The center of circle Q is on the y-axis, and the circle passes through  [#permalink]

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New post 10 Jun 2015, 18:30
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The center of circle Q is on the y-axis, and the circle passes through points (0, 7) and (0, –1). This tells us the circle's center, which is (0,3) and the radius, which is 4.

Circle Q intersects the positive x-axis at (p, 0). we can just use the equation for distance between two points. In this case, (0,3) and (p,0).

4=\(sqrt((0-3)^2 + (p-0)^2)\)
p=\(sqrt(7)\)

Answer:
(D) \(sqrt(7)\)
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Re: The center of circle Q is on the y-axis, and the circle passes through  [#permalink]

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New post 02 Dec 2015, 19:15
agree with D. if center of the circle is on y axis, then it must be the case that r=4 while the center is at 0,3. Now, we can draw a line from 0,3 to the point of intersection of the circle with x axis. the line will have a length of 4, since it is the radius of the circle.
we know 2 sides of a right triangle...we can find the 3rd side: 4^2 = 3^2 +x^2, where x is the length of the leg.
16=9+x^2 -> x=sqrt 7.
since the y-coordinate of the line is 0, then the x coordinate of the intersection of the circle must be sqrt 7.
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Re: The center of circle Q is on the y-axis, and the circle passes through  [#permalink]

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New post 28 Mar 2018, 04:55
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Re: The center of circle Q is on the y-axis, and the circle passes through &nbs [#permalink] 28 Mar 2018, 04:55
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