if a parabola whose length of latus rectum is 4a touches the coordinate axes the find the locus of its focus

Let (h,k) be the focus of the hyperbola, since it touches the axis tangent at the vertex should be

 and the equation of its directrix should be  and the perpendicular distance

from direcrtrix to tangent at vertex is equal to a.

therefore

locus of focus is

Thanks Regards,

Sunil Raikwar,

askIITians faculty.