Question

Suppose a tunnel for a road is in the shape of a semi-ellipse represented by the equation x^2/400+y^2/144=1 with measurements given in feet. Engineers havedecided that the tunnel must be twice as wide and 1.5 times as tall Write the equation that represents the new tunnel

Answer 1

In this case the formula of an ellipse is

`(x^2)/(a^2)+(y^2)/(b^2)=1`

In our case a helps to the wise and b with the tall

`a=\sqrt[]{400}=20`
`b=\sqrt[]{144}=12`

Then if we need twice the wide

`2a=2(20)=40`

and 1.5 the tall

`1.5(12)=18`

Therefore our new equation is

`(x^(2))/(1600)+(y^(2))/(324)=1`

ANSWER

`D\text{. }(x^(2))/(1600)+(y^(2))/(324)=1`