MATH SOLVE

2 months ago

Q:
# Identify the graph of the equation. What is the angle of rotation for the equation? (Picture below)

Accepted Solution

A:

Answer:The answer is hyperbola; with angle of rotation = 45° ⇒ answer (b)Step-by-step 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°