![(BEL 1)](/media/m/b/c/8/bc834529b87b9051776759f4bbdd709a.png)
A parabola
![P_1](/media/m/a/8/8/a886eaf7832af6b6b5f56f0ec9a97490.png)
with equation
![x^2 - 2py = 0](/media/m/8/7/d/87da4c440a3cdb0936de1554f7e36949.png)
and parabola
![P_2](/media/m/e/c/8/ec8662164615835e6c2307d72a487ec8.png)
with equation
![x^2 + 2py = 0, p > 0](/media/m/a/a/0/aa0922495bad5af06d11b013b6d13094.png)
, are given. A line
![t](/media/m/7/f/6/7f630d3904cfcd77d22bd7938423df6c.png)
is tangent to
![P_2.](/media/m/d/e/5/de5127ec91dc1afdd0cd625498d2265c.png)
Find the locus of pole
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
of the line
![t](/media/m/7/f/6/7f630d3904cfcd77d22bd7938423df6c.png)
with respect to
%V0
$(BEL 1)$ A parabola $P_1$ with equation $x^2 - 2py = 0$ and parabola $P_2$ with equation $x^2 + 2py = 0, p > 0$, are given. A line $t$ is tangent to $P_2.$ Find the locus of pole $M$ of the line $t$ with respect to $P_1.$