Answer:
Equation of Ellipse is [tex]\frac{x^{2} }{32} +\frac{y^{2} }{36} =1[/tex]
Step-by-step explanation:
Let's find the value for [tex]a^{2}[/tex] and [tex]b^{2}[/tex] to write the equation for vertical ellipse.
Here 'a' is the distance from center to one of the vertices.
"b" is the distance from center to one of the Co-vertices. We need to find this using formula [tex]a^{2} -b^{2} =c^{2}[/tex]
'c' is the distance between center to one of the Foci.
In this problem center is origin.
So, a =6(because distance between(0,0) and (0,6) is 6)
c= 2 (because distance between (0,0) and (0,2) is 2)
Plug in the known values into the formula [tex]a^{2} -b^{2} =c^{2}[/tex]
36-[tex]b^{2}[/tex]= 4
Subtract both sides 36
[tex]-b^{2}[/tex] = -32
Divide both sides by -1
[tex]b^{2}[/tex] =32
So, equation would be
[tex]\frac{x^{2} }{32} +\frac{y^{2} }{36} =1[/tex]
