Question

HELP PLEASE

Answer 1

General equation for an ellipse with the center (0,0) could be determined using
$\boxed{ \dfrac{x^{2}}{a^{2}}+ \dfrac{y^{2}}{b^{2}}=1}$
with stands for the length of the horizontal radius and b stands for the length of vertical radius

From the question above, we could draw informations:
b = 27 ft
one of the points on ellipse (x,y) = (24,9)

plug the numbers into the equation
$\dfrac{x^{2}}{a^{2}}+ \dfrac{y^{2}}{b^{2}}=1$
$\dfrac{24^{2}}{a^{2}}+ \dfrac{9^{2}}{27^{2}}=1$
$\dfrac{576}{a^{2}}+ \dfrac{81}{729}=1$
$\dfrac{576}{a^{2}}+ \dfrac{1}{9}=1$
solve for a²
$\dfrac{576}{a^{2}} =1-\dfrac{1}{9}$
$\dfrac{576}{a^{2}} =\dfrac{8}{9}$
$a^{2} =\dfrac{9}{8} \times 576$
a² = 648

Input the value of a² to the equation
$\boxed{ \dfrac{x^{2}}{648}+ \dfrac{y^{2}}{729}=1}$
This is the equation of the ellipse

Answer 2

Remark
The general equation for an ellipse is
$\frac{x^2}{a^2}+ \frac{y^2}{b^2}=1$ 

At the center, the the point is 0,27

Solving for the 
$\frac{0}{a^2} + \frac{27^2}{b^2} = 1$
or b^2= 27^2 * 1
Taking the square root of both sides 
b = 27

Now we need to use one more piece of information
The second point is (24,9) what that means is at the point x = 24, y = 9

Solving for that 
$\frac{24^2}{a^2}+\frac{9^2}{27^2}=1$

576/a^2 + 81/729 = 1    Subtract 81/729 from both sides
576/a^2 = 1 - 81/729 = 576/a^2 = (729 - 81)/729 = 648 /729

576/a^2 = 648/729     Cross multiply

648 a^2 = 729 * 576   Divide by 648
a^2 = 648            

Full equation for the ellipse and answer is

$\frac{x^2}{648}+ \frac{y^2}{729} = 1$