Question

Which point does not lie on the circle centered at A(3, 1) and passing through the origin (0, 0)?.

Answer 1

You have not provided the options, therefore, I cannot give you an exact solution.
However, I'll try to help you with the procedures.

To solve this question, we can simply get the equation of the circle. Any point that does not satisfy the equation will be the point you're looking for.

Now, the general form of the equation of the circle is:
(x-h)² + (y-k)² = r²
where:
(h,k) represent the coordinates of the center of the circle
r is the radius of the circle

We are given that:
The center of the circle is at (3,1). This means that:
h = 3 and k = 1
Therefore, the equation now is:
(x-3)² + (y-1)² = r²

Now, we need to get the radius. The radius can be calculated by getting the distance from the center of the circle and any point that lies on it.
We have the center at (3,1) and point (0,0) lying on the circle.
Therefore:
distance = r = $\sqrt{(x2-x1)^2 + (y2-y1)^2} = \sqrt{(0-3)^2 + (0-1)^2} = \sqrt{10}$

Based on the above, the equation of the circle is:
(x-3)² + (y-1)² = 10

I have attached a diagram of the circle.

Any point that does not satisfy this equation will not be lying on this circle

Hope this helps :)