Question 2 (Essay Worth 10 points) (03.05, 03.06 HC)

Question

A system of equations is made up of an ellipse and a hyperbola.

Part A: Create the equation of an ellipse centered at the origin, with a horizontal major axis of 8 units and a minor axis of 6 units. Show your work. (3 points)

Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (–7, 0), and asymptotes of  Show your work. (4 points)

Part C: Determine the domain of each conic section and use it to explain why there is no solution to the system. (3 points)

Answer 1

Part A)

x^2/4^2 +y^2/3^2 = 1 is the ellipse center at the origin

with axes 8 and 6,

semi axes = 8/2 =4 and 6/2= 3

or

x^2/16 + y^2/9 = 1

or

multiply by 9(16)

9x^2 + 16y^2 = 144