Answer:
5.25
Step-by-step explanation:
The fact that the graph crosses the x-axis means the hyperbola opens to the left and right. Hence its equation is ...
x^2/a - y^2/b = 1
The point (-2, 0) helps us find "a":
(-2)^2/a - 0/b = 1
4 = a
Then we can find "b" from the other fully-specified point.
(-3)^2/4 - 4^2/b = 1 . . . . . . substitute (-3, 4) for (x, y)
b = 16/(9/4 -1) = 64/5 . . . . solve for b
Then the third point will satisfy ...
t^2/4 - (5/64)·2^2 = 1 . . . . . . substitute (t, 2) for (x, y)
t^2 = 4·(1 +5/16) = 4 +5/4 . . . . solve for t^2
t^2 = 5.25
