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

Answer this Question
Related Questions
 geometry  A moving point is always equidistant from (3,2) and the line 2xy+2=...
 geometry  A moving point is always equidistant from (3,2) and the line 2xy+2=...
 Analytic Geometry  Please help me to solve this problem. Find the equation of ...
 maths pleaaaase  The point X and Y are 8cm apart Draw a scale drawing of the ...
 maths plse help me..  without using set square or protacter construct 1. ...
 Geo (locus)  I don't fully get this stuff but some of these I guessed on and ...
 Analytic Geometry  Find the equation of a locus of a point which moves so that ...
 geometry  what is the equation of the locus points equidistant from the lines y...
 geometry  Find the locus of a point which is equidistant from the origin and ...
 math  1) The Vietnam Memorial in Washington, DC is an angular wall. If you are ...