The equation 16x² - y² = 16 represents a hyperbola ⇒ 2nd answer
Step-by-step explanation:
The general form of the equation of a conic is
Ax² + Bxy + Cy² + Dx + Ey + F = 0, where A, B, C, D, E, and F
are constants
To find the type of conic that the equation represent find B² - 4AC
1. B² - 4AC < 0 and the conic is exist, then it's ellipse or circle,
if A = C, (non-zero) then it is a circle, if A ≠ C, then it is an ellipse
2. B² - 4AC = 0 and the conic is exist, then it's a parabola
3. B² - 4AC > 0 and the conic is exist, then it's a hyperbola
∵ The equation is 16x² - y² = 16
- Subtract 16 from both sides
∴ 16x² - y² - 16 = 0
∵ Ax² + Bxy + Cy² + Dx + Ey + F = 0
∴ A = 16 , B = 0 , C = -1 , D = 0 , E = 0 , F = -16
∵ B² - 4AC = (0)² - 4(16)(-1)
∴ B² - 4AC = 64
∵ 64 > 0
∵ B² - 4AC > 0
∴ The conic is hyperbola
The equation 16x² - y² = 16 represents a hyperbola
Learn more:
You can learn more about hyperbola in brainly.com/question/4054269
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