Find the Area of an Ellipse Given Shortest Distance and Longest Distance from a certain Focus to Circumference? [closed]

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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.

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1 Answer

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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 $\pi ab$

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