Solution: Because e=c/a= radical number (A 2+B 2)/A = radical number 5/2.

Square gain

(a^2+b^2)/a^2=5/4

4a^2+4b^2=5a^2

4b^2=a^2

So the curve equation can be set.

X 2/4-y 2 = a 2 or

y^2-x^2/4=a^2

Substitute (3, root number 2) respectively.

a^2=9/4-3=-3/4

a^2=3-9/4=3/4

So the equation is

x^2/4-y^2=-3/4

x^2/4-y^2=3/4

That is 4y 2-x 2 = 3.

Or x 2-4y 2 = 3.

Tangent line passing through (x0, y0) x 2+y 2 = r 2

x0*x+y0*y=r^2