Analytic geometry, distances

Question

Find the equation of the geometric place:

Whose distance to the point $(4,0)$ equals half the distance to the straight line $x=19$

Im using the formula for distance between points $P(4,0), Q(19,0)$ and an arbitrary line $l: d(l,P)=d(l,Q)/2$ but it gets me nowhere. Am I doing it right?

Welcome to Math Stack Exchange! To get the best help, it is needed that you at least show what you have tried. — wythagoras, May 08 '15 at 18:53

score 0 · Accepted Answer · answered May 08 '15 at 18:54

0

Hints:

$d((x,y),(4,0)) = \sqrt{(x-4)^2+y^2}$;
If $\ell: x = 19$, then $d((x,y),\ell) = |x-19| = \sqrt{(x-19)^2}$;
You want to look at $$d((x,y),(4,0)) = \frac{1}{2}d((x,y),\ell).$$

answered May 08 '15 at 18:54

Ivo Terek

77,665

Why isn't d((x,y),l) = sqrt((x-19)^2 + y^2) ? Sorry I suck at using mathjax – user239025 May 08 '15 at 19:05
$\ell$ is a vertical line. Draw the line and the point $(x,y)$. The distance is given by the length of a horizontal segment. – Ivo Terek May 08 '15 at 19:06

Analytic geometry, distances

1 Answers1