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mikemcgarry
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The center of circle Q is on the y-axis, and the circle passes through 26 Nov 2014, 11:48
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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) \(\sqrt{11}\)

For a set of Coordinate Geometry practice questions with solutions, visit this page:
https://magoosh.com/gmat/2013/gmat-quan ... questions/

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The center of circle Q is on the y-axis, and the circle passes through 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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The center of circle Q is on the y-axis, and the circle passes through 02 Dec 2015, 19:15
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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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The center of circle Q is on the y-axis, and the circle passes through 13 Sep 2019, 14:37
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Given that the two points (0,7) and (0,-1) are so far apart but lay on the circle, it is safe to assume the distance that separates them is the diameter and thus the midpoint of these two points will allow us to determine the radius.

(0+0)/2 = 0
(7-1)/2 = 3
midpoint = (0,3)

See plotted

If you plotted correctly you can plainly see the radius is 4.

This radius can be used to identify the point p,0 as 4 is the distance between 0,3 and any point on the circle.

4 = root((x2-x1)^2 + (y2-y1)^2)
16 = (p-0)^2 + (3-0)^2
16 = p^2 + 9
p^2= 7
p = root 7
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The center of circle Q is on the y-axis, and the circle passes through 09 Dec 2020, 00:32
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Given the Circle Intersects Points (0 , 7) and (0 , -1) and the Center must lie on the Y-Axis, we know that the Diameter of this Circle is given by the Length in Units from the Y-Coordinate of 7 ------> to the Y- Coordinate of -1

Diameter = 8

Radius = 4


The Center of the Circle is therefore 4 Units Down on the Y-Axis from Point (0 , 7)

Center is at - (0 , 3)


Equation for a Circle in the Coordinate Plane is given by an Equation of the Form:

(x - h)^2 + (y - k)^2 = (r)^2

----where the Coordinates (h , k) Represent the Center of the Circle and Variable r represents the Radius of the Circle---

The Equation for the Given Circle given Center (0 , 3) and Radius = r = 4:

(x)^2 + (y - 3)^2 = (4)^2


The Circle will cross the X-Axis when the Y value = 0. Substituting in Y = 0 to find the X-Coordinate of P:

(x)^2 + (0 - 3)^2 = (4)^2

(x)^2 = 16 - 9 = 7

Since the Question asks for the (+)Positive X-Intercept, P will be equal to:

sqrt(7)

(D)
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The center of circle Q is on the y-axis, and the circle passes through 28 Apr 2021, 13:34
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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) 7/3

(B) 4

(C) 5

(D) √7

(E) √11

midpoint: 0,3 --> Hence the radius is 4

4 = √ (p - 0)^2 + (0 - 3)^2
16 = p^2 + 9
p = √7

D
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