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In the xy-coordinate system, a circle with radius 30^(1/2)
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11 Dec 2018, 14:20
11 Dec 2018, 14:20
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Question Stats:
70% (02:27) correct
29% (02:24) wrong based on 48 sessions
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In the xy-coordinate system, a circle with radius \(\sqrt {30}\) and center (2,1) intersects the x-axis at (k,0). One possible value of k is.
A. \(2 + \sqrt{26}\)
B. \(2 +\sqrt{29}\)
C. \(2 + \sqrt{31}\)
D. \(2 + \sqrt{34}\)
E. \(2 + \sqrt{35}\)
A. \(2 + \sqrt{26}\)
B. \(2 +\sqrt{29}\)
C. \(2 + \sqrt{31}\)
D. \(2 + \sqrt{34}\)
E. \(2 + \sqrt{35}\)
Re: In the xy-coordinate system, a circle with radius 30^(1/2)
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12 Dec 2018, 09:26
12 Dec 2018, 09:26
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Carcass wrote:
In the xy-coordinate system, a circle with radius \(\sqrt {30}\) and center (2,1) intersects the x-axis at (k,0). One possible value of k is.
A. \(2 + \sqrt{26}\)
B. \(2 +\sqrt{29}\)
C. \(2 + \sqrt{31}\)
D. \(2 + \sqrt{34}\)
E. \(2 + \sqrt{35}\)
A. \(2 + \sqrt{26}\)
B. \(2 +\sqrt{29}\)
C. \(2 + \sqrt{31}\)
D. \(2 + \sqrt{34}\)
E. \(2 + \sqrt{35}\)
Explanation::
The distance (X) between two points (a,b) and (c,d) in a co ordinate plane is given by:
\(X = (\sqrt{(c - a)^2 + (d - b)^2}\)
Here,
\(X =\sqrt{30}\)
c = k and d = 0
a = 2 and b = 1
Therefore,
\(\sqrt{30} = \sqrt{(k - 2)^2 + (0 - 1)^2}\)
\(30 = (k - 2)^2 + 1\)
\((k - 2)^2 = 29\)
Solving for k;
\(K = 2 + \sqrt{29}\)
In the xy-coordinate system, a circle with radius 30^(1/2)
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15 Aug 2022, 19:25
15 Aug 2022, 19:25
1
More intuitively:
We have a right triangle with height 1 and hypotenuse sqrt(30).
Well, Pythagoras can give us a hand:
c^2 = (sqrt(30))^2 - 1^2
c^2 = 29
c = sqrt(29)
c is the length of the basis of the triangle. We just need to remember that we are departing from the point (2,0). So, just add 2 to get the coordinate.
2 + sqrt(29).
We have a right triangle with height 1 and hypotenuse sqrt(30).
Well, Pythagoras can give us a hand:
c^2 = (sqrt(30))^2 - 1^2
c^2 = 29
c = sqrt(29)
c is the length of the basis of the triangle. We just need to remember that we are departing from the point (2,0). So, just add 2 to get the coordinate.
2 + sqrt(29).
