Question 894112
Find the equation of the hyperbola which satisfies the given condition center (0,0) conjugate axis along x-axis, one focus at (0,sqrt(13) , equation of one directrix is y = 9sqrt(13)/13
***
Given hyperbola has a vertical transverse axis and center at the origin
Its standard form of equation: {{{y^2/a^2-x^2/b^2=1}}}
..
y=a/e=a/(c/a)=a^2/c
a^2=c*y=√13*9√13/13=9
c=√13
c^2=13
c^2=a^2+b^2
b^2=c^2-a^2=13-9=4
equation: {{{y^2/9-x^2/4=1}}}