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. \(2 + \sqrt{35}\)
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;
\(K = 2 + \sqrt{29}\)
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