Conic Questions

Questions (also sketch all)

• 1. What are the asymptotes and vertices of the hyperbola 4x^2-9y^2=2 .
• 2. What is the equation for an ellipse with the vertices: (2/3,0) , (-2/3,0) , (0,7/4) , (0,-7/4)
• 3. What are the aymptotes and vertices for 3xy=25
• 4. A hyperbola has the vertices (5,0) and (-5,0). It has the asymptotes y=3/5x and y=-3/5x. Find it's equation.

Answers (Diagrams from left to right)

• 
• 1. 2x^2 - 9/2y^2 = 1 , x^2/1/2 - y^2/2/9 :
• (x/root(1/2))^2 - (y/root(2/9)^2 = 1 ,
• Vertices: (1/root(2) , 0) , (-1/root(2) , 0)
• 2. (x/2/3)^2 + (y/7/4)^2 = 1 , same as: (3x/2)^2 + (4y/7)^2 = 1
• 3. 3xy = 5 (as root 25 for c^2) , xy=5/3
• Vertices: (5/3,5/3) , (-5/3,-5/3)
• Asymptotes: x=0 , y=0
• 4. (x/5)^2 - (y/3)^2 = 1