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SAT Math· difficulty 4/5

Does the line y=x+1y = x + 1 intersect the circle (x−2)2+(y−3)2=4(x-2)^2 + (y-3)^2 = 4?

  • A

    No

  • B

    Yes, in two points

    check_circle
  • C

    Cannot be determined

  • D

    Yes, in one point (tangent)

Explanation

Substitute y=x+1y = x + 1: (x−2)2+(x+1−3)2=4(x-2)^2 + (x+1-3)^2 = 4, so (x−2)2+(x−2)2=4(x-2)^2 + (x-2)^2 = 4, 2(x−2)2=42(x-2)^2 = 4, (x−2)2=2(x-2)^2 = 2. Two real solutions, so two intersections.

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