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Answer:
The standard form of a hyperbola with vertices and foci on the x-axis:
where:
- center: (h, k)
- vertices: (h+a, k) and (h-a,k)
- Foci: (h+c, k) and (h-c, k) where the value of c is c² = a² + b²
- Slopes of asymptotes:
The center of the given hyperbola is (0, 0), therefore:
Therefore are the vertices. From inspection of the graph,
.
Choose two points on the asymptote with the positive slope:
(0, 0) and (4, 6)
Use the slope formula to find the slope:
Use the <u>slopes of asymptotes</u> formula, compare with the slope found in part 2:
Therefore,
Substitute the found values of and
into the equation from part 1: