The point (7, 4) lies on a circle centered at the origin. Write the equation of the circle and state the radius.

Given:

The point (7, 4) lies on a circle centered at the origin.

To find:

The equation of the circle and the radius of the circle.

Solution:

Distance formula:

The point (7, 4) lies on a circle centered at the origin. So, the distance between the points (7,4) and (0,0) is equal to the radius of the circle.

The standard form of the circle is

           ...(i)

Where, (h,k) is the center of the circle and r is the radius of the circle.

Putting h=0, k=0 and in (ii), we get

Therefore, the equation of the circle is and its radius is .

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