identify the vertex and the length of the transverse axis is 10 units, and the length of the conjugate axis of the hyperbola
x^2/25-y^2/16=1
To identify the vertex and the lengths of the transverse and conjugate axes of a hyperbola, we need to first rewrite the equation of the hyperbola in the standard form:
(x - h)²/a² - (y - k)²/b² = 1
Where (h, k) represents the coordinates of the center of the hyperbola, a represents the distance from the center to the vertices (half the length of the transverse axis), and b represents the distance from the center to the co-vertices (half the length of the conjugate axis).
For the given equation x²/25 - y²/16 = 1, we can rewrite it in the standard form:
(x - 0)²/5² - (y - 0)²/4² = 1
Comparing this equation with the standard form, we can identify the following values:
- Center: (h, k) = (0, 0)
- Length of the transverse axis = 2a = 2 * 5 = 10 units
- Length of the conjugate axis = 2b = 2 * 4 = 8 units
Therefore:
- Vertex: The vertex of the hyperbola is the point (h, k), which is (0, 0).
- Length of the transverse axis: 10 units.
- Length of the conjugate axis: 8 units.