Question

On a coordinate plane, a circle has a center at (0, 0). Point (3, 0) lies on the circle.

Answer 1

Answer:

d

Step-by-step explanation:

Answer 2

Answer:

The correct option is;

No, the distance from (0, 0) to (2, √6) is not 3 units

Step-by-step explanation:

The given parameters of the question are as follows;

Circle center (h, k) = (0, 0)

Point on the circle (x, y) = (3, 0)

We are required to verify whether point (2, √6) lie on the circle

We note that the radius of the circle is given by the equation of the circle as follows;

$Distance \, formula = \sqrt{\left (x_{2}-x_{1} \right )^{2} + \left (y_{2}-y_{1} \right )^{2}}$

Distance² = (x - h)² + (y - k)² = r² which gives;

(3 - 0)² + (0 - 0)² = 3²

Hence r² = 3² and r = 3 units

We check the distance of the point (2, √6) from the center of the circle (0, 0) as follows;

$\sqrt{\left (x_{2}-x_{1} \right )^{2} + \left (y_{2}-y_{1} \right )^{2}} = Distance$

Therefore;

(2 - 0)² + (√6 - 0)² = 2² + √6² = 4 + 6 = 10 = √10²

$\sqrt{\left (2-0 \right )^{2} + \left (\sqrt{6} -0 \right )^{2}} = 10$

Which gives the distance of the point (2, √6) from the center of the circle (0, 0) = √10

Hence the distance from the circle center (0, 0) to (2, √6) is not √10 which s more than 3 units hence the point  (2, √6), does not lie on the circle.