How can I find an equation of a hyperbola given the vertices (-4,0)(4,0) passing trough the point (2 square root 7, 3)

Answer 1

it may help to plot the points and sketch the hyperbola

it's a horizontal hyperbola

general equation is x^2/a^2 - y^2/b^2 = 1

a =4

plug in the point (2sqr7, 3)

(2sqr7)^2/4^2 - 3^2/b^2 = 1

28/16 -9/b^2 = 1

7/4 - 9/b^2 = 1

7b^2 - 36 = 4b^2

3b^2 =36

b^2 = 36/3 = 12

x^2/16 - y^2/12 = 1 is the hyperbola