Answer:
The point lie outside the circle
Step-by-step explanation:
step 1
Find the distance between the center of the circle and the given point
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
(0,0) and (-3,-7)
substitute the values
[tex]d=\sqrt{(-7-0)^{2}+(-3-0)^{2}}[/tex]
[tex]d=\sqrt{58}\ units[/tex]
step 2
Compare the distance with the radius
If d=r ----> the point lie on the circle
If d > r -----> the point lie outside the circle
If d < r -----> the point lie inside the circle
we have
[tex]d=\sqrt{58}\ units[/tex]
[tex]r=\sqrt{53}\ units[/tex]
so
[tex]\sqrt{58}\ units > \sqrt{53}\ units[/tex]
[tex]d > r[/tex]
therefore
The point lie outside the circle
