Question

determine an equation and the radius for the circle that has its centre at the origin (0,0) passes through the point A 4-3

Answer 1

Given:

The center of the circle is at (0,0).

The circle passes through the point A(4,-3).

To find:

The radius and the equation of the circle.

Solution:

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

The radius of the circle is the distance between the points (0,0) and (4,-3).

`r=√((4-0)^2+(-3-0)^2)`

`r=√((4)^2+(-3)^2)`

`r=√(16+9)`

`r=√(25)`

`r=5`

So, the radius of the circle is 5 units.

The standard form of a circle is

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

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

Putting h=0, k=0, r=5, we get

`(x-0)^2+(y-0)^2=5^2`

`x^2+y^2=25`

Therefore, the radius of the circle is 5 units and the equation of the circle is
`x^2+y^2=25`.