Question

Complete the proof that the point (-2, V5 ) does or does not lle on the circle centered at the origin and containing the point (0,3). Part 1 out of 4 The radius of the circle is

Answer 1

We will have the following:

*First: We have that the equation of the circle will be given by:

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

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

*Second: We will replace the center of the circle and determine the radius:

`x^2+y^2=r^2`

*Third: We determine the radius of the circle by using the point given:

`(0)^2+(3)^2=r^2\Rightarrow r^2=9\Rightarrow r=3`

*Fourth: We have the following expression representing the circle:

`x^2+y^2=9`

So, we replace the point (-2, sqrt(5)) to determine whether or not it belongs to the circle, that is:

`(-2)^2+(\sqrt[]{5})^2=9\Rightarrow4+5=9\Rightarrow9=9`

Thus proving that the point (-2, sqrt(5)) does lie in the circle.