Find the standard equation of the circle whose center is on the straight line 2x-y-3 = 0 and passes through points (5,2) and (3, - 2) | Math enthusiast | Mathematical art

Find the standard equation of the circle whose center is on the straight line 2x-y-3 = 0 and passes through points (5,2) and (3, - 2)

The center of the circle is on the straight line 2x-y-3 = 0, y = 2x-3
Let the center of the circle be (a, 2a-3)
（5－a）^2+(2-2a+3)^2=r^2
(3 - a)^2 +(-2-2a＋3）^2=r^2
The solution is a = 2
r^2＝10
Center of circle (2,1)
Equation (X-2) ^ 2 + (Y-1) ^ 2 = 10

RELATED INFORMATIONS

1. Given the circle m, the center of the circle is on the line 2x + y = 0, and tangent to the line x + Y-1 = 0 at the point a (2, - 1), find the standard equation of the circle m
2. Given that the circle C passes through point a (2, - 1), the center of the circle is on the line 2x + y = 0 and tangent to the line x + y = 0, then the standard equation of circle C is
3. It is known that the center coordinate of the circle is (- 1,2) and tangent to the line 2x + Y-5 = 0 at point M. the standard equation of the circle is obtained
4. If the circle C passes through (2, - 1) and is tangent to the line x-y-1 = 0, and the center of the circle is on the line y = - 2x, then the standard equation of the circle C is
5. A circle passes through point P (2, - 1) and is tangent to the straight line X-Y = 1. The center of the circle is on the straight line y = - 2x
6. Given a circle passing through point P (2, - 1), the center of the circle is on L1: y + 2x = 0 and tangent to the line L2: x-y-1 = 0, the equation of the circle is obtained
7. Given that the circle passes through the point P (2, - 1) and is tangent to the straight line X-Y = 1, and its center is on the straight line y = - 2x, the equation of the circle is obtained
8. Find out the equation of the circle which passes through a (2, - 1) and is tangent to the line x + y = 1, and the center of the circle is on the line y = - 2x. (I) find out the standard equation of the circle; (II) find out the chord length AB of the intersection of the circle in (I) and the line 3x + 4Y = 0
9. When a circle passes through a (2,1) point and is tangent to a straight line X-Y = 0, and the center of the circle is on 2x-y = 0, the standard equation of the circle is obtained
10. As shown in the figure, in the rectangular coordinate system, point a is a point on the image of inverse scale function Y1 = KX, the positive half axis of ab ⊥ X axis is at point B, and C is the midpoint of OB; the image of primary function y2 = ax + B passes through two points a and C, and the Y axis is at point d (0, - 2), if s △ AOD = 4 (1) (2) observe the image, please point out the value range of X on the right side of y-axis when Y1 > Y2
11. The standard equation of a circle passing through points a (5,2) and B (3, - 2) with the center of the circle on the line 2x-y-3 = 0 I will find out the straight line L through AB, then find out the equation of AB vertical bisector, and then combine 2x-y-3 = 0 to find the center of the circle. But the answer is wrong. Is this method wrong?
12. It is known that the center of circle C is on the straight line 2x-y-3 = 0, and the standard equation of circle C can be obtained through points a (5,2), B (3,2)
13. Find the standard equation of the circle whose center is on the line 2x-y-3 = 0 and tangent to the X axis at the point (- 2,0) The standard equation of the circle whose center is on the line 2x-y-3 = 0 and tangent to the x-axis at the point (- 2,0)
14. The standard equation of a circle whose center is on 2x-y = 3 and tangent to two coordinate axes Two equations
15. Let the circle pass through point a (2, - 3), the center of the circle be on the straight line 2x + y = 0, and tangent to the straight line x-y-1 = 0, then the standard equation of the circle can be solved
16. The standard equation of the circle whose center is on the line y = - 2x and passes through the point a (0,1) and is tangent to the line x + y = 1
17. As shown in the figure, in the plane rectangular coordinate system xoy, the circle e with a diameter of 10 intersects the x-axis at points a and B, and intersects the y-axis at points c and D. the coordinates of points a and B are as follows: A (- 2,0), B (4,0). Try to find the coordinates of center E and points c, D Thank you）
18. As shown in the figure, if a circle is tangent to the x-axis in the plane rectangular coordinate system at point a (8,0), and intersects with the y-axis at points B (0,4), C (0,16), then the diameter of the circle is______ ．
19. In the rectangular coordinate system as shown in the figure, a and B are two points on the x-axis, and the circle with ab as the diameter intersects the y-axis at C. suppose that the analytical formula of the parabola passing through a, B and C is y = xx-mx + N, and the sum of the two reciprocal of the equation xx-mx + n = 0 is - 2 (1) Find the value of n (2) Find the analytical formula of this parabola (3) Let a straight line parallel to the x-axis intersect the parabola at two points E and F. ask if there is a circle with the diameter of line segments E and f just tangent to the x-axis? If so, find out the radius of the circle; if not, explain the reason
20. In the plane rectangular coordinate system, there are two straight lines, y = 3 / 5x + 9 / 5 and y = - 3 / 2x + 6. Their intersection point is m. The first line intersects with X axis at point a, and the second line intersects with X axis at point a Intersection with X axis at point B (1) Find the coordinates of two points a and B; (2) Using the image method to solve the equations; {3x-5y = - 93x + 2Y = 12 (3) Find the area of △ mAb)