sat-dog

- 2+ - 2= 2 Choice C is correct. The graph of the equation ^x hh ^y kh r in the xy-plane is a circle with center ^h,kh and a radius of length r. The radius of a circle is the distance from the center of the circle to any point on the circle. If a circle in the xy-plane intersects the y-axis at exactly one point, then the perpendicular distance from the center of the circle to this point on the y-axis must be equal to the length of the circle’s radius. It follows that the x-coordinate of the circle’s center must be equivalent to the length of the circle’s radius. In other words, if the - 2+ - 2= 2 graph of ^x hh ^y kh r is a circle that intersects the y-axis at exactly one = -4 2+ -9 2=16 point, then r h must be true. The equation in choice C is ^x h ^y h , -4 2+ -9 2=42 - 2+ - 2= 2 or ^x h ^y h . This equation is in the form ^x hh ^y kh r , where = = = 4,9 h 4, k 9, and r 4, and represents a circle in the xy-plane with center ^ h = and radius of length 4. Substituting 4 for r and 4 for h in the equation r h = = yields 4 4 , or 4 4, which is true. Therefore, the equation in choice C represents a circle in the xy-plane that intersects the y-axis at exactly one point. Choice A is incorrect. This is the equation of a circle that does not intersect the y-axis at any point. Choice B is incorrect. This is an equation of a circle that intersects the x-axis, not the y-axis, at exactly one point. Choice D is incorrect. This is the equation of a circle with the center located on the y-axis and thus intersects the y-axis at exactly two points, not exactly one point.