SOLUTION: Describe the collection of points in a plane so that the distance from each point to the point (5, 0) is five-fourths of its distance from the line x = 16/5
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Question 1128793: Describe the collection of points in a plane so that the distance from each point to the point (5, 0) is five-fourths of its distance from the line x = 16/5
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!
The instruction "describe" is not specific; so let's just find the equation of the locus of points.
The distance of a point (x,y) from (5,0) is
The distance of a point (x,y) from x = 16/5 is
The locus described is the set of points for which the distance from (5,0) is 5/4 the distance from x = 16/5:
Okay; so this is a recognizable locus.
The locus is a hyperbola with center at the origin; branches opening right and left; transverse axis (through the two vertices) length 2*4=8; conjugate axis (through the center perpendicular to the transverse axis) length 2*3 = 6.
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