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It is known that the center of circle C is tangent to the line l2:4x + 3Y + 14 = 0 on the line L1: x-y-1 = 0, and the straight line l3:3x + 4Y + 10 = 0 is obtained. The chord length is 6, and the equation of circle C is obtained
The center of the circle C is on the line L1: x-y-1 = 0, a-b-1 = 0, a-b-1 = 0, a-b-1 = 0, ∵ the circle C is tangent to the line l2:4x + 3Y + 14 = 0, r = | r = | 4A + 3B + 3B + 14 | 5,
The center of the circle is on 2x-y + 1 = 0, tangent to 3x-4y + 9 = 0, and cut 4x-3y + 3 = 0, the chord length is 2. Find the equation of circle
Center C on 2x-y + 1 = 0 √
C(a,1+2a)
Tangent to 3x-4y + 9 = 0
r=|3a-4-8a+9|/5=|1-a|
And the chord length obtained by cutting 4x-3y + 3 = 0 is 2
The distance from C to 4x-3y + 3 = 0 h = | 4a-3-6a-3 | / 5 = | 2a-6 | / 5
r^2=h^2+(2/2)^2
21a^2-26a-36=0
A=
C（ ）
Given that the center of circle C cuts the straight line 3x + 4Y + 3 = 0 on the y-axis, the chord length is 8. And it is tangent to the line 3x-4y + 37 = 0, the equation of circle C is solved
The center of the circle is on the y-axis. The coordinates of the center of the circle C are (0, b) tangent to the straight line 3x-4y + 37 = 0, r = | 3 * 0-4 * B + 37 | / 5 the distance from the center of the circle to 3x + 4Y + 3 = 0, d = | 3 * 0 + 4 * B + 3 | / 5 half chord length is 4
Find the chord ab of the line 3x + y-6 = 0 and the circle x ^ 2 + y ^ 2-2y + 4 = 0
Circle: x? + y? - 2y-4 = 0
x²+(y-1)²=5
Radius of center (0,1) = √ 5
The distance from the center of a circle to a straight line d = ｜ 1-6 / √ (9 + 1) = √ 2 / 2
According to Pythagorean theorem
Radius r, D and half chord length form a right triangle
So AB = 3 √ 2
The straight line L: x-2y + 5 = 0 intersects the circle C: x ^ 2 + y ^ 2 + 2x-4y = 0. Find the length of chord ab of line L cut by circle C
x^2＋y^2＋2x－4y=0
(x+1)^2+(y-2)^2=5
Center (- 1,2), radius = √ 5
Distance from center of circle to line L = | - 1-2 × 2 + 5 | / √ (1 square + 2 square) = 0
therefore
The line goes through the center of the circle, so
Chord AB = diameter = 2 √ 5
What are the midpoint and chord length of chord AB cut by the line L: x + Y-1 = 0 and the circle C: x? + y? - 2x-2y-6 = 0 Need process
The circle C: x 2 + y 2 - 2x-2y-6 = 0, that is (x-1) ^ 2 + (Y-1) ^ 2 = 8,
2, 2,
Distance from center of circle to x + Y-1 = 0:
d=|1+1-1|/√2=√2/2,
Chord length: 2 √ [(2 √ 2) ^ 2 - (√ 2 / 2) ^ 2] = √ 30 / 2,
∵ the circle and the straight line are both about the line y = x,
The midpoint of the chord is on the line x + Y-1 = 0 and also on y = X,
The midpoint of chord (1 / 2, 1 / 2)
We know that the center P of a circle is on the straight line y = x, and the circle is tangent to the line x + 2y-1 = 0, and the chord length obtained by cutting the Y axis is 2
Let the coordinates of the center of the circle be p (a, a), then the radius r = | a + 2A − 1 | 5 = | 3a − 1 | 5
As shown in the figure, the circle center of ⊙ P is on the straight line y = x and tangent to the line x + 2y-1 = 0. The chord AB length obtained by the circle cutting the positive half axis of Y axis is 2. Find the equation of the circle
Let the center of ⊙ p be on the straight line y = x, let the equation of the circle be (x-a) 2 + (Y-A) 2 = R2 (a > 0),
∵⊙ P is tangent to the straight line x + 2y-1 = 0, and the chord AB length obtained from the positive half axis of the circle's Y-axis is 2,
∴|3a−1|
5 = R, and A2 + (| AB)|
2) 2 = R2, that is, A2 + 1 = (3a − 1) 2
5，
The results show that: (2a + 1) (A-2) = 0,
A ＞ 0, a = 2, R=
5，
The equation of ⊙ P is (X-2) 2 + (Y-2) 2 = 5
It is known that the center of the circle is on the straight line y = x, tangent to the line x + 2Y -- 1 = 0, and the chord length obtained by cutting the Y axis is 2?
Let the circle be (x-a) ^ 2 + (Y-A) ^ 2 = R ^ 2
The chord length obtained by cutting Y axis is 2 = > R ^ 2 = 1 + A ^ 2
Tangent to x + 2Y -- 1 = 0 = > | a + 2a-1 | / radical 5 = R
The simultaneous solution gives a = - 1 / 2 or 2
The equation is (X-2) ^ 2 + (Y-2) ^ 2 = 5
Or (x + 1 / 2) ^ 2 + (y + 1 / 2) ^ 2 = 5 / 4
It is known that the circle whose center is on the straight line X-Y + 1 = 0 is tangent to the line x + 2Y = 0, and the chord length cut by the circle on the x-axis and y-axis is 1:2, so we can find the equation of the circle,
The equation is: (x-a) ^ 2 + (y-a-1) ^ 2 = R ^ 2 = R ^ 2 ^ 2 (x-a) ^ 2 + (y-a-1-1) ^ 2 = R ^ 2 = R ^ 2 the distance between the center of a circle and the straight line x + 2Y = 0 is r, that is: | a + 2A + 2A + 2 / / √ 5 = R -- > R ^ 2 = (3a + 2) ^ 2 / 5Y = 0, (x-a) ^ 2 = R ^ 2 - (a + 1) ^ 2, X-axis chord length = 2 √ (R ^ 2 - (a + 1) ^ 2) x = 0, (y-a-1) ^ 2 = r = R ^ 2 = R ^ 2 = R ^ 2 = R ^ 2 = R ^ 2 = R ^ 2 = R ^ 2 A ^ 2, chord length on Y axis =
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