Hyperbola and ellipse have a common point of intersection, F 1 (0, - 5) f 2 (3,4) is an intersection of the asymptote of hyperbola and ellipse Ideas, principles, the best detailed. Thank you~

Hyperbola and ellipse have a common point of intersection, F 1 (0, - 5) f 2 (3,4) is an intersection of the asymptote of hyperbola and ellipse Ideas, principles, the best detailed. Thank you~

The focus is on the y-axis
c=5
y^2/b^2-x^2/a^2=1
x^2/m^2+y^2/n^2=1
n>m
n^2=m^2+5^2
P is on the ellipse
So 9 / m ^ 2 + 16 / (m ^ 2 + 25) = 1
9(m^2+25)+16m^2=m^2(m^2+25)
m^4=9*25
m^2=3*5=15
n^2=40
Ellipse x ^ 2 / 15 + y ^ 2 / 40 = 1
Asymptote y = ± (B / a) x
P is on the asymptotic line
4=(b/a)*3
b=4a/3
a^2+b^2=c^2=25
25a^2/9=25
a^2=9,b^2=16
y^2/16-x^2/9=1