Question

Circle G has a diameter whose endpoints are (9, 4) and (1, 2). The standard equation of Circle

Gis
O (X - 5)2 + (y - 3)2 = 8.5
O (X - 5)2 + (y - 3)2 = 17
O (x - 3)2 + (y - 5)2 = 17
O (y - 5)2 + (x-3)2 = 8.5

Answer 1

The standard equation of Circle G with diameter endpoints at (9, 4) and (1, 2) is (x - 5)^2 + (y - 3)^2 = 17, with (5, 3) being the circle's center and 17 as the radius squared.

Step-by-step explanation:

The question relates to finding the correct standard equation for Circle G given its diameter's endpoints. To find the center of Circle G, we take the midpoint of the endpoints (9, 4) and (1, 2). The midpoint formula is ((x1 + x2)/2, (y1 + y2)/2), which yields (5, 3). The radius can be found using the Pythagorean theorem on the differences in the x and y coordinates of the endpoints, which are 8 and 2, respectively, giving us a radius squared (r^2) of 4^2 + 1^2 = 17. Therefore, the correct standard equation of a circle with center (5, 3) and radius squared of 17 is: (x - 5)^2 + (y - 3)^2 = 17.

When discussing circles, it's essential to remember the relationship between the circle's perimeter (circumference) and its radius since the circumference is 2πr. Likewise, the area of a circle is πr^2, which is relevant when considering how a circle fits within a square. In such a case, the circle's diameter equals the side length of the square.