Problem Solving (PS) | Re: If line L y=3+x forms tangent to a circle with center at (1,-4), what

Given, Line y =x+3 => x -y +3 = 0 and Center (1,-4)
The radius will be equal to the perpendicular distance from the center to the tangent:
radius =\(\frac{|1*1 + (-1)(-4) +3|}{(\sqrt{(1^2 + 1^2)})}\)
radius = 8/\(\sqrt{2}\)
Radius =4*\(\sqrt{2}\)

Let the line which will be parallel to the tangent: x-y+k = 0
So, the perpendicular distance to the new line from the center will also be equal to the radius.

Thus,
4*\(\sqrt{2}\) =\( \frac{|1*1 + (-1)(-4) +k|}{(\sqrt{(1^2 + 1^2)})} \)
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