g The background of a printed company logo is in the shape of an ellipse with height 20 inches and width 24 inches. Find an equation for the ellipse and use it to find the vertical width, in inches, of the logo background at a distance of 3 inches horizontally from the center.

Equation is x^2/576+y^2/400=1

Vertical height is 19.84inches

Step-by-step explanation:

The equation of an ellipse with horizontal major axis with center at (0,0) is x^2/a^2+y^2/b^2=1

From the question, a=24 and b=20

Therefore the equation of the ellipse = x^2/24^2+y^2/20^2=1

= x^2/576+y^2/400=1

To calculate vertical height y:

y^2/400=1 - x^2/576

y^2 = (1 - x^2/576) * 400

y=20√ (1 - x^2/576)

At x=3 inches from the centre

y=20√1-0.0156

y=20*0.9922

y=19.84inches