Question

The equation of an ellipse is given by

x^2 / 9+ y^2 / 6 = 1.
a. Sketch the graph of the ellipse.
b. Rewrite the equation of the ellipse in complex form.

Answer 1

a). Image

b).
`(x^(2) )/(a^(2))+ (y^(2) )/(b^(2))=1\\(x^(2) )/(3^(2))+ (y^(2) )/((√(6)) ^(2))=1`

Explanation:

a).

`(x^(2))/(9)+ (y^(2))/(6)=1\\ (y^(2))/(6)=1-(x^(2))/(9)\\y^(2) = 6- (6x^(2))/(9)\\y=√(6)-  (√(2) )/(√(3))*x\\x=0\\y=√(6)`≅2.44

`x=3\\y=√(6)-(√(2))/(√(3)) *3\\ y=2.44-2.44\\y=0`

Those points see in the image

(0,2.44) and (3, 0)

b).

`((x-h)^(2) )/(a^(2)) +((y-k)^(2) )/(b^(2))=1\\(h,k)=(0,0) \\a=√(9) =3\\b=√(6) \\(x^(2) )/(3^(2) ) +(^(2) )/(√(6) ^(2) )=1`