A window has the shape of a parabola above and a circular arc below. Find the area of the window.

Question

https://myopenmaths3.s3.amazonaws.com/qimages/windowparbolacircl.png

From x- axis to top of parabola is 4.84 feet

The length of one end of the parabola to the other is 14 feet

The last length is 14.9 feet

Find the distance from the x-axis to the top of the circle. ______ feet

Write the equation of the circle _______  

Write the equation of the parabola _______

Find the area of the window _________ ft^2

Answer 1

top of circle is 1.75 ft above x-axis reference

eq of parabola y=(-4.84/49)x²+4.84

eq of circle x²+(y+13.15)²=14.9²

area of curved window approximately 29.2 sq ft.

Answer 2

Strategy:

Find the equation for the parabola, p(x), and then find the equation for the circle, c(x).

A = 2∫₀⁷ p(x) - c(x) dx. Using limits of 0 and 7 and doubling since the curves are symmetric around the y-axis.

p(x) = a(x-h)²+k where (h,k) is the vertex which you can get from the image. Solve for a when y=0, x=7

c(x): (x-h)²+(y-k)²=r² where (h,k) is the center of the circle

solve for y = c(x). From image, r = 14.9, h=0. You can solve for k by setting y=0 and x= 7.

The value from the x-axis to the top of the circle is r-k.