Asked by vaughn
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?
Please help. how to do this problem?
Answers
Answered by
Steve
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 = √[(x-5)^2 + (y-3)^2]
(3x+5y+5)^2 = 10((x-5)^2 + (y-3)^2)
9x^2+30xy+25y^2+30x+50y+25 = 10x^2+10y^2-100x-60y+340
-x^2 + 30xy + 15y^2 + 130x + 110y - 315 = 0
Hmm. That's an hyperbola. I was expecting a parabola. Better check my algebra.
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 = √[(x-5)^2 + (y-3)^2]
(3x+5y+5)^2 = 10((x-5)^2 + (y-3)^2)
9x^2+30xy+25y^2+30x+50y+25 = 10x^2+10y^2-100x-60y+340
-x^2 + 30xy + 15y^2 + 130x + 110y - 315 = 0
Hmm. That's an hyperbola. I was expecting a parabola. Better check my algebra.
Answered by
JP
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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