Ineed ! write the equation of the circle with center (0, 0) and (−4, 5) a point on the circle. a) x2 + y2 = 1 b) x2 + y2 = 9 c) x2 + y2 = 41 d) x2 + y2 = 81

Standard equation for a circle is: (x -h)² + (y - k)² = r²
(h,k) is the center which is given to be: (0,0) so you just need the radius.
The radius is the distance from the center to the point (-4,5) on the edge.

Use the distance formula

d = √[(-4 - 0)² + (5 -0)²]
d = √[16 + 25]
d = √[41]

radius is √[41]
so the equation for the circle is: x² + y² = 41