In an ellipse, I am given that the shortest distance from one focus to the circumference is $1.5$. Then the longest distance from that focus to the circumference of $4.5$. What is the area of the ellipse?
I'm pretty sure the semi-major axis would be $3$, but I do not know how to calculate the semi-minor axis now.
Hint...if you already know that $a=3$ then you probably also have that the eccentricity $e=\frac 12$
In which case you can use $$b^2=a^2(1-e^2)$$ and the area is $\pi ab$