Question

An elliptical arch is constructed which is 6 feet wide at the base and 9 feet tall in the middle. Find the height of the arch exactly 1 foot in from the base of the arch. looking for direction with what ellipse equation is and how to approach this problem

Answer 1

Place the center of the ellipse at (0,0)
You know that the semi-major axis (height) is a=9
the semi-minor axis (half the width) is b=3
So that means that
x^2/9 + y^2/81 = 1
Now just find y when x = 2

Answer 2

Place the center of the ellipse at (0,0)
Since the major axis is equal to 2a and the middle is 9 feet tall, a = 4.5
Since the minor axis is equal to 2b and the length is 6 feet, b = 3
We now have enough information to put the equation into standard form for a vertical ellipse (we do vertical ellipse equation because the major axis is on the y-axis that goes up and down)

(x-h)^2/b^2 + (y-k)^2/a^2=1

x^2/9 + y^2/20.25=1

Now solve for y when x = 1 using algebra. Whatever you get for y is your answer.