Final answer:
The intercept points of a circle with a radius of 49 are (0, 49), (0, -49), (49, 0), and (-49, 0) corresponding to the y-intercepts and x-intercepts respectively. Option d) (±7, ±7) is incorrect as it does not satisfy the circle's equation.
Step-by-step explanation:
The student's question asks for the coordinates of the intercept points of a circle with a given equation and a radius of 49. The equation of a circle centered at the origin with radius r is x² + y² = r². In this case, if the radius is 49, the equation of the circle would be x² + y² = 49². To find the intercept points, we set either x or y to zero and solve for the other variable.
- For the x-intercept: y = 0, the equation becomes x² = 49². Solving for x gives x = ±49, hence the x-intercepts are (49, 0) and (-49, 0).
- For the y-intercept: x = 0, the equation becomes y² = 49². Solving for y gives y = ±49, thus the y-intercepts are (0, 49) and (0, -49).
The coordinates of the intercept points are therefore (0, 49), (0, -49), (49, 0), and (-49, 0), which means options a), b) and c) are correct. Option d) is incorrect since the points (±7, ±7) do not satisfy the equation of the circle with a radius of 49.