a circle is centered at the origin and contains the point (4,0). Would (2 square root 2,-square root 6) also be on the circle

Answer:circle do not contains point (2√2 , -6) Step-by-step explanation:Equation of circle:The centre-radius form of the circle equation is in the format (x – h)² + (y – k)² = r²with the centre being at the point (h, k) and the radius being "r"Plug in values given the question to find the radius of circle (4-0)² + (0 - 0)² = r² r² = 16 r = √16 r  = 4 To find coordinates(2√2 , -6) is in the circle Simply plug in the x and y from your point (2√2 , -6)If the the answer is greater than r², then the point lies outside of the circle else they are in the circle (x – 0)² + (y – 0)² ≤ 16 ((2√2)² – 0)² + ((-6)² – 0)² ≤ 16  8 + 36 ≤ 16  44 ≤ 16 False  Hence, (2√2 , -6) don't lie in or on the circle.