Posted by vaughn on Monday, January 7, 2013 at 8:56am.
A moving point is always equidistant from (5,3) and the line 3x+y+5=0. What is the equation of its locus?
Please help. how to do this problem?

geometry  Steve, Monday, January 7, 2013 at 10:02am
the distance of the point (h,k) from the line ax+by+c=0 is
d = ah+bk+c/√(a^2+b^2)
the distance between two points (x1, y1) and (x2, y2) is √[ (x2  x1)^2 + (y2  y1)^2]
Let the moving point be (x,y). Substituting the values we have:
3x+5y+5/√10 = √[(x5)^2 + (y3)^2]
(3x+5y+5)^2 = 10((x5)^2 + (y3)^2)
9x^2+30xy+25y^2+30x+50y+25 = 10x^2+10y^2100x60y+340
x^2 + 30xy + 15y^2 + 130x + 110y  315 = 0
Hmm. That's an hyperbola. I was expecting a parabola. Better check my algebra.

geometry  JP, Sunday, January 25, 2015 at 10:04pm
why did you put square root of 10 in the denmntor? the formula is Ax1+by1+c/+squareroot of A^2+B^2 SUBSTITUTING THE X AND Y IT WILL YOU A REAL NUMBER

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