Answer the situational problem involving ellipse and hyperbola

Question

A road passes through a tunnel in the form of a semi-ellipse. In order to widen the road to accomodate more traffic,engineers must design a larger tunnel that is twice as wide and 1.5 times as tall as the original tunnel. The design for the original tunnel can be modelled by the equation x²/100 + y²/64 = 1,measured in feet,write an equation for the design of the layer tunnel

Answer 1

Standard equation for an elipse:

x²/a² + y²/b² = 1

 

If a>b then the major axis is horizontal. The "a" is the x-distance from center to side, the "b" is the y-distance from center to top. Kind of like a radius for a circle but they are not equal in an elipse.

 

The given equation for the elipse:

 

x²/100 + y²/64 = 1

 

x²/10² + y²/8² = 1

 

The width (horizontal, x-distance) of the tunnel needs to be twice as wide. 10*2 = 20

The height (vertical, y-distance) of the tunnel needs to be 1.5 times taller. 8*1.5 = 12

 

Replace the a/b values

 

x²/20² + y²/12² = 1

 

x²/400 + y²/144 = 1

Answer 2

I got the numbers backwards. My apologies