Question

Which point lies on the circle represented by the equation (x - 1)2 + (y - 3)2 = 72 ?O (-1,4)(0,7)(1,3)(8,3)

Answer 1

We are given a set of points and a circle defined by equation:

$(x-1)^2+(y-3)^2=7^2=49$

A point that lies on the circle is a point whose x and y coordinate are solutions to the equation above. This means that if I have a point (a,b) that it's on the circle and take x=a and y=b then the equation above turns into 49=49. So let's test every point we have.

First, (-1,4) so x=-1 and y=4:

$\begin{gathered} (-1-1)^2+(4-3)^2=49 \\ (-2)^2+(1)^2=49 \\ 4+1=5=49 \end{gathered}$

5=49 is not correct so point (-1,4) isn't on the circle.

Now point (0,7):

$\begin{gathered} (0-1)^2+(7-3)^2=49 \\ (-1)^2+(4)^2=49 \\ 1+16=17=49 \end{gathered}$

Again, 17=49 is not correct so this point isn't on the circle either.

(1,3):

$\begin{gathered} (1-1)^2+(3-3)^2=49 \\ (0)^2+(0)^2=49 \\ 0=49 \end{gathered}$

0=49 is also incorrect so (1,3) is another point that doesn't belong to the circle.

Finally for (8,3) we have:

$\begin{gathered} (8-1)^2+(3-3)^2=49 \\ 7^2+0=49=49 \end{gathered}$

We have 49=49 which is a correct statement so point (8,3) is part of the circle which means that the last option is the right one.