Question

A circle of radius 5 touches the coordinate axes in the first quadrant. If the circle makes one complete roll on X-axis along the positive direction of x-axis, then its equation in the new position is​

Answer 1

Answer:

The equation of the circle in the new position will be

$(x - (5+10\pi ))^{2} + (y-5)^{2} = 25$

Step-by-step explanation:

As the radius of the circle is 5, So, the x, y coordinates are (5, 5).

Both x and y coordinates are positive as the circle is placed in the first quadrant. When the circle moves to the x-axis and complete one rotation, It will cover the distance equal to the circumference

$2\pi r$ = $10\pi$

The total distance covered by the circle will be

5 + $10\pi$

So, the new coordinates of the circle will be

((5+$10\pi$), 5)

The circle equation is

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

Hence the circle equation for the new position will be

$(x - (5+10\pi ))^{2} + (y-5)^{2} = (5)^{2}$

$(x - (5+10\pi ))^{2} + (y-5)^{2} = 25$

I hope this answer may help you