Parabola having focus $(1,2)$ touches both axes. Find the equation of directrix.
As perpendicular tangents meet at directrix, the directrix passes through origin. So the directrix has equation of the form $y+mx=0$. How do I get the $m$ ?
$\begingroup$
$\endgroup$
1
-
1$\begingroup$ Related : math.stackexchange.com/questions/767631/… $\endgroup$– lab bhattacharjeeJan 8, 2016 at 14:48
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
Use the property: The reflection of focus about any tangent of the parabola lies on the directrix.
Hence, taking it's reflection along Y axis, we get $(-1,2)$ and taking it's reflection along X axis, we get $(1,-2)$. Since both the points lie on the directrix of the equation, the equation of the directrix is the line joining these two points.
The directrix hence comes out as $y+2x=0$.
answered Jan 8, 2016 at 16:23
$\begingroup$
$\endgroup$
Hint: The directrix must be perpendicular to the line joining the points (0,0) and (1,2).
