![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
The equation of circle passing through M (5,2), n (3,2) and its center on the straight line y = 2x-3 is obtained
Let the center of the circle be (x, y),
The center of the circle is on the vertical bisector x = 4 of the line Mn, and the center of the circle is on the straight line y = 2x-3
x＝4
y＝2x−3 ，
The center of the circle is (4,5), r =
(5−4)2+(2−5)2＝
Ten
∴（x-4）2+（y-5）2=10
The equation of a circle passing through the points a (1,1), B (- 3,5) and the center of the circle is on the straight line 2x + y + 2 = 0
If the abscissa of the center C is a, then the ordinate is - 2-2a,
According to | Ca | = | CB = R, a
So know the center and radius of the circle, and then get the equation of the circle!
Answer: a = - 2
(x+2)^2+(y-2)^2=10
Find the equation of circle whose center is on the straight line 2x-y + 3 = 0 and passes through points (5,2) and (3, - 2)
Let a (5,2), B (3, - 2)
Let the coordinates of any point on the line be (x, y), then
(x-5)²+(y-2)²=(x-3)²+(y+2)²
X + 2y-4 = 0
The solution of the equation and the known linear equation shows that O (- 2 / 5,11 / 5) is the center of the circle
Square of radius: OA? = (5 + 2 / 5) 2 + (2-11 / 5) 2 = 146 / 5
Therefore, the equation of the circle is as follows:
(x+2/5)²+(y-11/5)²=146/5
It is known that the circle passes through point a (2, - 1), and its center is on the straight line 2x + y = 0 and tangent to the straight line x-y-1 = 0
Let the equation of a circle be (x-a) 2 + (y-b) 2 = R2 (r > 0). ∵ the center of the circle is on the line 2x + y = 0,
The equation of the circle passing through point a (3,2) whose center is on the line y = 2x and tangent to the line y = 2x + 5 is obtained
Let the coordinates of the center of the circle be (a, 2a), then
According to the meaning of the title, | 2A − 2A + 5|
5＝
(a−3)2+(2a−2)2=r，
The solution is: a = 2, R=
5 or a = 4
5，r=
5，
The equation of the circle is: (X-2) 2 + (y-4) 2 = 5 or (x-4)
5）2+（y-8
5）2=5．
The equation of a circle passing through two points a (- 1,4) B (3,2) and its center on the straight line x + y + 5 = 0 is solved
Linear AB equation: 2Y + X-7 = 0
AB midpoint coordinates: (1,3)
Vertical equation in AB: y = 2x + 1
Linear equation of circle center: x + y + 5 = 0
The coordinates of the center of the circle: (- 2, - 3)
Circle radius r = 5 √ 2
The equation of circle: (x + 2) 2 ＋ (x + 3) 2 = 50
The equation of a circle passing through a (1, - 1), B (- 1,1) and its center on the straight line x + Y-2 = 0 is?
Let the standard equation of a circle be (x-a) 2 + (y-b) 2 = R 2
It is known that: (1-A) 2 + (- 1-B) 2 = R 2 (1)
(-1-a)²+(1-b) ²=r²,…… II.
a+b-2=0,…… 3.
① - 2 gives: - 4A + 4B = 0, and when combined with ③, a = b = 1
So r = 2
The equation of the circle is (x-1) 2 + (Y-1) 2 = 4
Find the equation of the circle whose center is on the straight line x + y + 3 = 0 and passes through the point (4,3) (- 2,1)
Given that the midpoint of two points is (1,2), the slope is 1 / 3
The equation of vertical bisector is: Y-2 = - 3 (x-1), i.e., y = - 3x + 5
When it is combined with the straight line x + y + 3 = 0, x = 4, y = - 7
The center of the circle is (4, - 7)
The radius is | - 7-3 | = 10
The equation of the circle is: (x-4) 2 + (y + 7) 2 = 100
Find the equation of the circle whose center is on the circle (x-3 / 2) ^ 2 + y ^ 2 = 2 and tangent to the X axis and the straight line x = - 1 / 2 It is known that P1 (x1, Y1) and P2 (X2, Y2) are two points on the straight line with slope K |P1p2 | = √ (1 + k? 2) times | x1-x2| = √ (1 + K 2) times √ ((x1 + x2) 2 - 4x1x2)
1. The distance from the center to the tangent is equal to the radius, so the distance from the center to y = 0 and from the center to x = - 1 / 2 are the same. So the center of the circle is on the bisector of the angle between the two lines, so the angle between the center and the positive direction of the X axis is 45 degrees or 135 degrees, so the slope is 1 or - 1, and the vertex is the intersection point (- 1 / 2,0) of the two lines, so the bisector of the angle is y = x + 1 / 2 or y = - X
The center of the circle is on the Y axis, the radius is 1, and the equation of the circle passing through the point (1, 2) is () A. x2+（y-2）2=1 B. x2+（y+2）2=1 C. （x-1）2+（y-3）2=1 D. x2+（y-3）2=1
Solution 1 (direct method): let the coordinates of the center of the circle be (0, b),
From the meaning of the title
(o−1)2+(b−2)＝1，
B = 2, so the equation of circle is x2 + (Y-2) 2 = 1
Therefore, a
Solution 2 (combination of number and shape): from the distance between the point (1,2) and the center of the circle is 1, it is easy to know that the center of the circle is (0,2),
So the equation of circle is x2 + (Y-2) 2 = 1
Therefore, a
Solution 3 (verification method): replace the points (1, 2) into the four selection branches,
Exclude B, D, and since the center of the circle is on the y-axis, exclude C
Therefore, a
RELATED INFORMATIONS
- 1. If the center of the circle is on the Y-axis and the circle passing through the point (3,1) is tangent to the x-axis, then the equation of the circle is
- 2. Find the equation of the line with root sign 10 which is perpendicular to the straight line x + 3Y + 5 = 0 and the distance from the point P (- 1.0) is three fifths times
- 3. Given that the straight line L passes through the point (- 2,3) and the distance from the origin to the line L is 2, then the equation of the line L is______ .
- 4. The linear equation passing through point a (1,2) and the maximum distance from the origin is______ .
- 5. What is the equation for all lines passing through the point (- 3,1) and the line farthest from the origin
- 6. There is a chord in a circle with radius 1. If its length is root 3, then what is the degree of circumference angle of this string Can we do it without trigonometric functions?
- 7. The ratio of the length of the two arcs divided by the chord is 2:7, and the degree of the circumferential angle of the chord is______ .
- 8. In the circle center o with radius of 50 mm, chord AB is 50 mm long. Calculate the degree of angle AOB and calculate the distance from point O to ab by using the vertical diameter theorem
- 9. If the circumference of a sector with radius 2 is equal to the arc length of its semicircle, then the central angle of the sector is___ Radian, the sector area is___ .
- 10. If a circle is divided into four sectors a, B, C and D, and the area ratio of sector ABCD is 2:1:4:5, what degree is the center angle of the largest sector
- 11. Given the circle C; x 2 + y 2 = 12 and the straight line 4x + 3Y = 25, what is the probability that the distance between any point a on circle C and line L is less than 2?
- 12. Circle x ^ 2 + y ^ 2-2y-1 = 0 the equation of symmetric circle with straight line x-2y-3 = 0 is
- 13. Find the equation of the circle with point (1,2) as the center and the line 4x + 3Y minus 35 equal to 0 Can we add the process I can't understand it=
- 14. The straight line L is parallel to the straight line 4x-3y + 5 = 0, and the distance between the point P (2, - 3) and the line L is 4
- 15. If there are two different points on the circle x ^ 2 + y ^ 2 = R ^ 2 [R > 0], the distance from the straight line 4x-3y + 25 = 0 is equal to 1 Detailed, thank you
- 16. Find the equation of circle whose center is on the straight line X-Y-4 = 0 and passes through the intersection of two circles x2 + y2-4x-3 = 0, X2 + y2-4y-3 = 0 If we want the coordinates of the center of the circle and the length of the radius, I have listed the formula and can't calculate it I can't work out the radius
- 17. The equation for a symmetric circle with a straight line x + y = 0 is
- 18. Given that the moving circle m is tangent to the straight line y = 2 and circumscribed with the fixed circle C: x 2 + (y + 3) 2 = 1, the trajectory equation of the moving circle m is obtained
- 19. The straight line passing through the right focus x ^ 2-y ^ 2 = 1 intersects hyperbola at a, B, AB as the diameter of the circle. If the circle passes through the origin, what is the slope k?
- 20. Given the circle C: x ^ 2 + y ^ 2-2x-4y + 1 = 0 and the straight line L: ax-y + 3 = 0, if the circle C is symmetric about the line L, find the value of A