1. Tardigrade
  2. Question
  3. Mathematics
  4. Points A and B are selected on the graph of x2+2 y=0 so that the triangle A B O is equilateral. The length of the side of the triangle is ('O' is the origin)

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Q. Points $A$ and $B$ are selected on the graph of $x^2+2 y=0$ so that the triangle $A B O$ is equilateral. The length of the side of the triangle is ('O' is the origin)

Conic Sections

Solution:

$y=-\frac{x^2}{2}$
$\tan 30^{\circ}=\frac{2 t }{ t ^2} \Rightarrow \frac{1}{\sqrt{3}}=\frac{2}{ t } \Rightarrow t =2 \sqrt{3} $
$l( OP )=4 \sqrt{3} $