Question

4. The centre of a circle is at (0,0) and a point on the circle is (4,3). Find
the length of the radius of the circle.​

Answer 1

Given,

Centre of the circle (0,0)

A point on the circle (4,3)

To Find,

The radius of the circle.

Solution,

We can use the distance formula to calculate the radius of the circle.

As the distance between the centre and any point on the circle is equal to the radius of the circle.

Radius = √(x₂-x₁)²+(y₂-y₁)²

Where, (x₂,y₂) and (x₁,y₁) are the two given points.

Radius = √(4-0)²+(3-0)²

Radius = √25

Radius = 5

Hence, the radius of the circle is 5 units.

Answer 2

Recall that the radius of the circle is: $r=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }$

Given:

The center of the circle is $(0,0)$

And a point lies on the circle is $(4,3)$

Radius is the distance between the center of the circle and any point on the circle.

$r=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }$

where, $x_{1}=0, x_{2}=4, y_{1}=0, y_{2}=3$

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

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

$r=\sqrt{16+9 }$

$r=\sqrt{25 }=5.$

Therefore: The radius of the circle is $r=5.$