Question

Find the equation of the circle of radius 2 and which touches both the coordinate axes.​

Answer 1

Answer:

The center of the circle with radius 2 in the initial position will be (2,2)

Since, it makes complete rotation along X-axis, its new co-ordinate will be (2+4π,2)

Therefore, equation of circle will be (x−2−4π)  

2

+(y−2)  

2

=4

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

where (a,b) is the center of the circle and r is the radius.

In your case, a=0 , b=0 , and r=7 .You add an additional restriction, however, that you only want the bottom half.

How can we formally restrict the range, so that we only have the bottom half? By solving for y, we get y=49−x2−−−−−−√ , which is the top half of the circle (why?). Since we want the bottom half, we wish to flip the half-circle over the x-axis, and we do so by letting f(x) become −f(x) resulting in:

y=−49−x2−−−−−−√ .

As an extension, how would we use a similar principle to get the right and left half of the circle instead?