2 circles are tangent each other and be x-axis above. What is the slop

Question

GEOMETRY.jpg 2 circles are tangent each other and be x-axis above. What is the slope of the line that passes through 2 centers of 2 circles? A. 2/√96 B. 1/√6 C. 1/2√3 D. 1/√3 E. 2√6 * A solution will be posted in two days.

Kurtosis · Answer

Slope = Change in Y/Change in X

Change in Y = 6 - 4 = 2

The length of line joining 2 centres = 6 + 4 = 10

Change in X =  \sqrt{10^2 - 2^2}  =  \sqrt{96}

Slope =  \frac{2}{\sqrt{96}}

Answer: A

bethebest · Answer

Can you please explain how you got Change in X = square root of 10^2-2^2
I thought change in X should be the distance between the two perpendiculars dropped from the centers of both the circles, and this difference would be 10. Please suggest what I am doing wrong.

Kurtosis · Answer

Consider a perpendicular line drawn from the centre of the smaller circle to the radius of the larger circle (Call it as 'a').

We know that hypotenuse = Distance between the line joining the two centres = 10

The other side = 2

By pythagoras theorem,  a^2 + 2^2  =  10^2  --> a = \sqrt{96}

bethebest · Answer

Thank you so much for a prompt response. This is very helpful

MathRevolution · Answer

2 circles are tangent each other and be x-axis above. What is the slope of the line that passes through 2 centers of 2 circles?

A. 2/√96
B. 1/√6
C. 1/2√3
D. 1/√3
E. 2√6

Attachment:

2 circles.jpg [ 10.93 KiB | Viewed 4536 times ]

Just like the picture above, d=√96 is derived from d^2=(10^2)-(2^2)=96. Then, the slope of the line that passes through 2 centres=length of YZ/length of XZ. Thus, the slope is 2/√96. Therefore, the answer is A.

Temurkhon · Answer

why do we need to find length between centers? We need to find slope of line

Slope=rise/run

rise=6-4=2
run=4+6=10

So, slope is 2/10=1/5

Kurtosis · Answer

Change in x is not 10. The centers of the two circles are different. You have to apply pythagoras theorem to determine the change in x.

Temurkhon · Answer

change in X coordinates is the length of horizontal line from one point to other. Here it is 10

Kurtosis · Answer

The radius of the two circles (4 and 6) forms a line whose slope has to be determined. You are assuming the combined radius of the line itself as the change in x value.

Temurkhon · Answer

Ah, I see, circles make me crazy. Thanks

Abi1995 · Answer

Slope = Change in Y/Change in X= 2

The length of line joining 2 centres = 6 + 4 = 10

Calculate, Change in X and Slope

Answer: A

Posted from my mobile device

Doryhihii · Answer

Hi  Bunuel , could you please help me for this question? Thank you.

bumpbot · Answer

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2 circles are tangent each other and be x-axis above. What is the slop

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2 circles are tangent each other and be x-axis above. What is the slop

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