Final answer:
The equation of the circle centered at the origin and passing through the point (-3,4) is x^2 + y^2 = 25, where 5 is the radius of the circle. we arrive at the equation of the circle: x2 + y2 = 25.
Step-by-step explanation:
The student has asked to find the equation of a circle that is centered at the origin and passes through the point (-3,4). Since the circle is centered at the origin, the equation of the circle can be written in the standard form x2 + y2 = r2 where r is the radius of the circle. To find the radius, we use the distance formula to calculate the distance from the center (0,0) to the point (-3,4), which is the radius of the circle.
The distance formula is √((x_2 - x_1)2 + (y_2 - y_1)2). Substituting the coordinates, we get the radius r = √((-3 - 0)2 + (4 - 0)2) = √(9 + 16) = √25 = 5. Therefore, the radius of the circle is 5 units.
Plugging this value into the equation, we arrive at the equation of the circle: x2 + y2 = 25.