Question

Знайдіть геометричне місце центрів кіл, які проходять через дві дані точки.

Answer 1

Ответ:

геометричним місцем центрів кіл які проходять через дві дані точки є серединний перпендикуляр до відрізка

Объяснение:

Answer 2

Geometric locus of centers of circles passing through two given points

To find the geometric locus of centers of circles passing through two given points, we can use the concept of perpendicular bisectors. The perpendicular bisector of a chord of a circle passes through the center of the circle. Therefore, if we find the perpendicular bisector of the line segment joining the two given points, the locus of the centers of circles passing through these points will be the perpendicular bisector.

Here's how we can find the equation of the perpendicular bisector:

1. Let the two given points be A(x1, y1) and B(x2, y2). 2. The midpoint of the line segment AB is M, which can be found using the following formulas: - x-coordinate of M: (x1 + x2) / 2 - y-coordinate of M: (y1 + y2) / 2 3. The slope of the line passing through points A and B can be found using the formula: - slope = (y2 - y1) / (x2 - x1) 4. The slope of the perpendicular bisector is the negative reciprocal of the slope of the line AB. Therefore, the slope of the perpendicular bisector is: - perpendicular_slope = -1 / slope 5. Using the point-slope form of a line, we can write the equation of the perpendicular bisector: - y - y-coordinate of M = perpendicular_slope * (x - x-coordinate of M)

By finding the equation of the perpendicular bisector, we have determined the geometric locus of the centers of circles passing through the two given points.

Example: Let's say the two given points are A(2, 3) and B(5, 7). We can find the equation of the perpendicular bisector and determine the locus of the centers of circles passing through these points.

1. Midpoint M: - x-coordinate of M: (2 + 5) / 2 = 3.5 - y-coordinate of M: (3 + 7) / 2 = 5 2. Slope of line AB: - slope = (7 - 3) / (5 - 2) = 4 / 3 3. Slope of perpendicular bisector: - perpendicular_slope = -1 / (4 / 3) = -3 / 4 4. Equation of perpendicular bisector: - y - 5 = (-3 / 4) * (x - 3.5)

Therefore, the geometric locus of the centers of circles passing through points A(2, 3) and B(5, 7) is given by the equation: y - 5 = (-3 / 4) * (x - 3.5).

Please note that the search results did not provide specific snippets related to finding the geometric locus of centers of circles passing through two given points. However, the explanation provided above is a standard geometric concept that can be found in geometry textbooks and online resources.