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:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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

$r=\sqrt{(4-0)^2+(-3-0)^2}$

$r=\sqrt{(4)^2+(-3)^2}$

$r=\sqrt{16+9}$

$r=\sqrt{25}$

$r=5$

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 $x^2+y^2=25$.