Chapter 1.4, Problem 49AYU

To determine

To find: the equation of the wheel

Answer to Problem 49AYU

The equation of the wheel is $x^2+{\left(y-139\right)}^2=15625$

Explanation of Solution

Given:

Height $=264$ $feet$

Diameter $=250$ $feet$

Calculation:

To find the equation of the wheel if the center of the wheel is on the $y-axis$

The maximum height is $264feet$ and the diameter is $250$ $feet$ , then the bottom of wheel is $264-250=14$ $feet$ above the ground.

Now the radius of wheel is $125feet$ .Now substituting these values in standard form of equation of circle. The equation wheel is,

  ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

  ${\left(x-0\right)}^2+{\left(y-139\right)}^2={\left(125\right)}^2$

  $x^2+{\left(y-139\right)}^2=15625$

Conclusion:

Hence, the equation of the wheel is $x^2+{\left(y-139\right)}^2=15625$