Question

A wooden plaque is in the shape of an ellipse with height 30 centimeters and width 22 centimeters. Find an equation for the ellipse and use it to find the horizontal width, in centimeters, of the plaque at a distance of 4 centimeters above the center point.

Answer 1

Answer:

Explanation:

height of Ellipse $=30 cm$  

i.e. $2 a=30$

Width of Ellipse $=22 cm$

i.e. $2 b=22$

Equation of a vertical Ellipse is

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

$a=15 ,b =11$

$\frac{x^2}{11^2}+\frac{y^2}{15^2}=1$

at $y=4 cm$

$\frac{x^2}{11^2}+\frac{4^2}{15^2}=1$  

$x=\frac{11}{15}\times \sqrt{15^2-4^2}$

$x=10.6 cm$