Answer:
The answer is hyperbola; with angle of rotation = 45° ⇒ answer (b)
Explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
- xy = -2.5
∵ A = 0 , B = 1 , C = 0
∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0
∴ B² - 4AC > 0
∴ The graph is hyperbola
* To find the angle of rotation use the rule:
- cot(2Ф) = (A - C)/B
∵ A = 0 , B = 1 , C = 0
∴ cot(2Ф) = 0/1 = 0
∴ 2Ф = 90°
∴ Ф = 45°
* The answer is hyperbola; with angle of rotation = 45°