i need help with my homework pls!

Question

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

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 vertical major axis of 12 units and a minor axis of 6 units. Show your work.

Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (–5, 0), and asymptotes of  Show your work.

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

Answer 1

Part A:

Center at (0,0)

Vertex at (0,6) and (0,-6), a = 6

Co Vertex at (3,0) and (-3,0), b = 3

(x^2)/(b^2) + (y^2)/(a^2) = 1 because the major axis is vertical

(x^2)/9 + (y^2)/36 = 1

Part B:

Center at (0,0)

Vertex at (5,0) and (-5,0), a = 5

b = 8 from the slope of the asymptotes

(x^2)/(a^2) - (y^2)/(b^2) = 1 because transverse axis is horizontal

(x^2)/25 - (y^2)/64 = 1

Part C:

Domain of ellipse is [-3,3]

Domain of hyperbola is (-infinity,-5] U [5,infinity)

There is no overlap so there are no common points and therefore no solution to the system.