SOLUTION: Find the value of k if the distance from the point (2,1) to the line 5x+12y+k=0 is 2.

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Question 942471: Find the value of k if the distance from the point (2,1) to the line 5x+12y+k=0 is 2.
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
12y=-5x-k
y=-(5/12)x-k/12
The general point of the line is (x, -(5/12)x-k/12 )

sqrt%28%28x-2%29%5E2%2B%28-%285%2F12%29x-k%2F12-1%29%5E2%29=2

Several algebra steps to find k.

The steps done on paper gave
169x%5E2%2B%2810k-576%29x%2Bk%5E2%2B24k%2B164=0, a quadratic equation in the variable, x, still using the unknown constant, k.

You need the discriminant of that to be zero or greater.
%2810k-576%29%5E2-4%2A169%28k%5E2%2B24k%2B164%29%3E=0
still not finished but you should continue from this.