Answer to Question #144627 in Analytic Geometry for Bonevie tutor

Question

A whispering gallery has a semislliptical chilling that is 10m high and 32m. How high is the ceiling above the two foci?

Answer 1

$\text{We have the equation of an ellipse with semiaxes a= 32 and b =10}$

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1; a^2=b^2+c^2$

$\text {where }c \text{ half the focal length. }$

$\text{for }x =c \text{ value }y \text{ is the desired value}$

$y^2= b^2(1-\frac{x^2}{a^2})$

$\text {for } x=c;\ y^2=b^2(1-\frac{a^2-b^2}{a^2})=\frac{b^4}{a^2}$

$y=\frac{b^2}{a}=3.125$

Answer: 3.125 m