A racetrack is in the shape of an ellipse 80 ft long ans 40 ft wide. what is the width 10 ft from the side?

Question

A racetrack is in the shape of an ellipse 80 ft long ans 40 ft wide. what is the width 10 ft from the side?

Answer 1

An ellipse whose major and minor axis intersect  at the origin is given by the formula;

x^2/A^2 + y^2/B^2 = 1

If x = 0, y = 40/2 = 20, Hence B = 20

If y =0, x = 80/2 = 40, Hence A = 40

Thus the equation of the given ellipse is;

x^2/40^2 + y^2/20^2 = 1

If x = 40 - 10 = 30

y^2 = (1-30^2/40^2)20^2 = 175

y = 13.229

The width 2y = 26.458 ft

Answer 2

wkt eq of an ellipse is x^2/a^2 + y^2/b^2 = 1

which is centered at the origin

where a and b are major and minor axes respectively

ie length and width respectively

if a = 80

b= 40

x= 80 - 10 =70  (ref is always origin and they said frm the side)

y=sqrt(b^2 * (1-x^2/a^2))

ie y = sqrt(40^2 * (1- 70^2/80^2))

then solving the equation we get y = 19.365

I hope it helps