Question

2. Find an equation of the ellipse with vertices (0, 6) and eccentricity e = ½

Answer 1

so it is vertical right

Answer 2

We have vertices (0,\(\pm 6\) )--> a = 6
and e =\(\dfrac{c}{a}\rightarrow c = ea =1/2*6=3\)
another formula for ellipse: \(c^2= a^2-b^2\rightarrow b^2=a^2-c^2 =36-9 =25\)
Therefore, the equation of the ellipse is \(\large \dfrac{x^2}{25}+\dfrac{y^2}{36}=1\)