sat-dog

The correct answer is 5. The standard form of an equation of a circle in the - 2+ - 2= 2 xy-plane is ^x hh ^y kh r , where h, k, and r are constants, the coordinates of the center of the circle are ^h,kh, and the length of the radius of the -2 2+ -9 2= 2 circle is r. It′s given that an equation of the circle is ^x h ^y h r . 2,9 Therefore, the center of this circle is ^ h. It’s given that the endpoints of a 2,4 2,14 diameter of the circle are ^ h and ^ h. The length of the radius is the distance from the center of the circle to an endpoint of a diameter of the circle, which can be found using the distance formula, ^x1- x2 h 2+ ^y1- y2 h 2 . 2,9 2,4 Substituting the center of the circle ^ h and one endpoint of the diameter ^ h 2-2 2+ 9-4 2 02+52 in this formula gives a distance of ^ h ^ h , or , which is equivalent to 5. Since the distance from the center of the circle to an endpoint of a diameter is 5, the value of r is 5.