Determine the equation of the hyperbola.

A) x²/9 -y²/4 = 1

Step-by-step explanation:

The distance from center to one vertex is half the difference of the distances from a point to either focus. That is, the distance from center to the vertex is 3 on the x-axis, so the x-term is (x/3)² = x²/9.

In the picture, ...

... c² = a² + b²

The problem statement tells us c = √13, so we know c² = 13. Then ...

... b² = c² - a² = 13 -9 = 4

and the y-term is y²/4.

Thus, the equation is ...

... x²/9 - y²/4 = 1

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You knew that was the correct choice as soon as you knew the x-term.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)