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Circle has an equation and radius of 49. Where will it intercept?

What are the coordinates of the intercept points of the circle with the equation and a radius of 49?
a) (0, 49)
b) (±49, 0)
c) (0, -49)
d) (±7, ±7)

User Joecks
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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.

User Shankar Cheerala
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8.2k points

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