Question

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

Answer 1

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:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

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.

`r=√((0-7)^2+(0-4)^2)`

`r=√((-7)^2+(-4)^2)`

`r=√(49+16)`

`r=√(65)`

The standard form of the circle is

`(x-h)^2+(y-k)^2=r^2` ...(i)

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

Putting h=0, k=0 and
`r=√(65)` in (ii), we get

`(x-0)^2+(y-0)^2=(√(65))^2`

`x^2+y^2=65`

Therefore, the equation of the circle is
`x^2+y^2=65` and its radius is
`r=√(65)`.