A circle with center (h, k), in which k = 2h, lies tangent to the y-ax

Question

A circle with center (h, k), in which k = 2h, lies tangent to the y-axis in in the (x, y) coordinate system. What is the distance from the origin to the center of the circle, in terms of k ?

A.  (k\sqrt{3)}/2 
B.  (k\sqrt{5)}/2 
C. k
D. k  \sqrt{3} 
E. k  \sqrt{5}

chetan2u · Answer

Let us draw the sketch first as per the info..

If we can draw the sketch, we are almost 90% there..Tangent means that a point of the circle lies on the y-axis.
This point on y-axis, the center of the circle and the origin will make a RIGHT angled triangle.

Distance =  \sqrt{k^2+h^2}=\sqrt{k^2+(k/2)^2}=\sqrt{5k^2/4}=\sqrt{5}*\frac{k}{2}

B

EgmatQuantExpert · Answer

Solution

Given  
 • A circle is present in the (x, y) coordinate system, whose center is (h, k)
• The circle is tangent to the y-axis
• Also, h = 2k, or k = h/2

To Find  
 • The distance from the origin to the center of the circle, in terms of k

Approach & Working  
 https://e-gmat.com/blogs/wp-content/uploads/2019/02/circle.png 
As we can see in the figure, angle OAC = 90° (as the circle is tangent to the y-axis)

Therefore, as per Pythagoras Theorem,
 •  OC^2 = OA^2 + AC^2 = k^2 + \frac{k^2}{4} = \frac{5k^2}{4}  
 Or, OC = k \sqrt{5}/2

Hence, the correct answer is option B.

https://e-gmat.com/blogs/wp-content/uploads/2016/12/Geometry-Ability-Quiz-4-e1480581478957.png

Archit3110 · Answer

k=2h
center ( h,k)
use the distance formula Sqrt( y2-y1)^2+(x2-x1)^2 
 and determine the distance from origin (0,0) to center of circle
= > k * sqrt5/2
IMO B

energetics · Answer

1) Draw a diagram to get an idea of how to solve
2) Plug in numbers for h and k, h=2 k=4 
3) Solve using pythagorean theorem, 2²+4² = hypotenuse² --> hyp = 2√5
4) Plug into answers, if k=4 then it's clearly B.

A circle with center (h, k), in which k = 2h, lies tangent to the y-ax

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A circle with center (h, k), in which k = 2h, lies tangent to the y-ax

Prep Toolkit

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