Answer:
Step-by-step explanation:
Given that vertex of the hyperbola is
(0,10) and(0,-10)
Hence the hyperbola will have equation of the form
[tex]\frac{y^2}{a^2} -\frac{x^2}{b^2} =1[/tex]
Since vertex has y coordinate as 10, we have a =10
So equation would be[tex]\frac{y^2}{10^2} -\frac{x^2}{b^2} =1[/tex]
Since asymptotes are y =±5x/4
we have equation of both asymptotes is
[tex]y^2-\frac{25x^2}{16} =0\\y^2/25-x^2/16 =0\\y^2/100-x^2/64 =0[/tex]
Since hyperbola will have equations same as asymptotes except with difference of constant terms as 1 instead of 0, we have
equation as
[tex]\frac{y^2}{100} -\frac{x^2}{64} =1[/tex]
