Answer:
y² / 81 - x² / 19 = 1
Step-by-step explanation: See Annex ( vertices and foci in coordinates axis)
The equation in standard form for the hyperbola is:
x² / a² - y²/b² = 1 or y²/a² - x² / b² = 1
In cases of transverse axis parallel to x axis or y axis respectively.
As per given information in this case hyperbola has a transverse axis parallel to y axis the equation is
y²/a² - x² / b² = 1
a is a distance between center and vertex therefore a = 9
c is a distance between center and a focus c = 10
and b will be:
c² = a² + b² ⇒ b² = c² - a² ⇒ b² = (10)² - (9)² ⇒ b² = 100 - 81
b = √19
And the equation in standard form is:
y² / a² - x² / b² = 1
y² / ( 9 )² - x² / √(19)² ⇒ y² / 81 - x² / 19 = 1
