Asked by huhhf3;q
Which of the following could be the graph of 4x^2-9y^2-36=0? brainly
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Answered by
GPT-5 mini
AI
Rewrite the equation:
4x^2 - 9y^2 - 36 = 0 ⇒ 4x^2 - 9y^2 = 36 ⇒ x^2/9 - y^2/4 = 1.
This is a hyperbola centered at (0,0) with transverse axis along the x‑axis (opens left and right). Features to look for:
- Vertices at (±3, 0).
- No real y‑intercepts (x=0 gives y^2 = −4).
- Asymptotes: y = ±(2/3)x.
So pick the graph that is a horizontal hyperbola centered at the origin with vertices at x = ±3 and asymptotes y = ±(2/3)x.
4x^2 - 9y^2 - 36 = 0 ⇒ 4x^2 - 9y^2 = 36 ⇒ x^2/9 - y^2/4 = 1.
This is a hyperbola centered at (0,0) with transverse axis along the x‑axis (opens left and right). Features to look for:
- Vertices at (±3, 0).
- No real y‑intercepts (x=0 gives y^2 = −4).
- Asymptotes: y = ±(2/3)x.
So pick the graph that is a horizontal hyperbola centered at the origin with vertices at x = ±3 and asymptotes y = ±(2/3)x.
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