Answer:
C
Step-by-step explanation:
First find the equation of the circle
the general formula for a circle (x-h)² + (y-k)² = r² where (h=0, k=0) are the coordinates of the center and r is the radius that we do not know
the distance between the center (0, 0) and the point (3,5) is the radius
distance formula d² = (x2-x1)² +(y2-y1)² where (x1=0,y1=0) and (x2=3, y2=5)
d² = (3-0)² + (5-0)² = 3² +5² = 9+ 25 = 34 =r²
(x-0)² + (y-0)² = 34 ; x²+y² =34 is the equation of the circle
Second check if any of the points are on the circle by substituting x and y with de given coordinates.
A. for (-2, 6) we have (-2)²+6² =34 so 4+36 =34 false
B. for (6, -√5) we have 6²+(-√5)² =34 so 36+5=34 false
C. for (1, √33) we have 1²+(√33)² =34 so 1+33 =34 true
D. for (-2√2, 4) we have (-2√2)²+4² =34 so 8+16=34 false
