Respuesta :
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;
[tex]Distance \, formula = \sqrt{\left (x_{2}-x_{1} \right )^{2} + \left (y_{2}-y_{1} \right )^{2}}[/tex]
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;
[tex]\sqrt{\left (x_{2}-x_{1} \right )^{2} + \left (y_{2}-y_{1} \right )^{2}} = Distance[/tex]
Therefore;
(2 - 0)² + (√6 - 0)² = 2² + √6² = 4 + 6 = 10 = √10²
[tex]\sqrt{\left (2-0 \right )^{2} + \left (\sqrt{6} -0 \right )^{2}} = 10[/tex]
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.
