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What is the chord length of the straight line y = radical 3x cut by the circle x? + y? - 4Y = 0?
x²+y²-4y=0
x^2+(y-2)^2=4
The distance from the center of the circle to the straight line is: 2 / √ 4 = 1
The radius is 2
So the half chord length is √ (2 ^ 2-1) = √ 3
So the chord length is 2 √ 3
Given that the circle is tangent to two straight lines X + y + 5 = 0, x + y = 7 = 0, the chord length cut on the line 3x-4y = 0 is 2 root sign 17, and the equation of the circle is solved
Because the straight line x + y + 5 = 0, x + Y-7 = 0 is parallel, so the diameter of the circle is the distance between two straight lines, so d = | 5 + 7 | / √ 2 = 6 √ 2R = 3 √ 2. Let the standard equation of circle be: (x-a) ^ 2 + (y-b) ^ 2 = (3 √ 2) ^ 2 = 18. The chord length of the circle cut on the line 3x-4y = 0 is 2, and the distance from the circle to the straight line is 3a-4b / 5
Given that X and y are real numbers, and y = x + the square of the root 4-x + (the square of the root x-4) - 1, find the root sign 3x + 4Y
The number under the root sign should be meaningful, all ≥ 0
So x-4 ≥ 0
x^2-4≥0
Then x ^ 2-4 = 0
x=±2
X + 2 as denominator, X ≠ - 2
So x = 2
y=-1/4
So √ 3x + 4Y = √ 3 * 2-4 * 1 / 4 = √ 5
The straight line 3x-4y + 1 = 0 is cut by the circle whose radius is root 5 and whose center is on the line y = 2x-1. The chord length is 4. Find the equation of the circle
Distance from center of circle to straight line d = √ (5-4) = 1
Let the center of the circle be (a, 2a-1)
∴|3a-8a+1|/5=1
∴|5a-1|=5
∴a=6/5 a=-4/5
/ / 2a-1 = 7 / 5 or - 13 / 5
The circular equation is
(x-6/5)²+(y-7/5)²=5
Or (x + 4 / 5) 2 + (y + 13 / 5) 2 = 5
The line passes through point a (5,5), and is cut by the square of circle x squared y = 25, the root sign 5 with chord length of four times is obtained, and the equation of straight line is solved
The straight line is y = - 2x / 5. 3. Let the line Y-5 = K (X-5)... And then the distance from the center of the circle to the straight line, and the hook strand is fixed
Given that the circle C: x ^ 2-4x + y ^ 2-3 = 0, the chord length of the straight line passing through point (4,5) is cut by circle C and the chord length is 2 times the root sign 3, then the equation of the straight line is?
Circle C: (X-2) ^ 2 + y ^ 2 = 7
Let the linear equation passing through the point (4,5) be Y-5 = K (x-4), that is, y = KX + 5-4k
The distance from center C to straight line d = | 2K + 5-4k| / radical (k ^ 2 + 1)
There is also d ^ 2 + [(2 root sign 3) / 2] ^ 2 = 7
That is, (2k-5) ^ 2 / (k ^ 2 + 1) = 7-3 = 4
4k^2-20k+25=4k^2+4
k=21/20
The equation is y = 21 / 20x + 5-84 / 20 = 21 / 20x + 4 / 5
The other linear equation is x = 4
The radius of the circle is known to be The center of the circle is on the line y = 2x, and the chord length of the circle cut by the line X-Y = 0 is 4 2. Find the equation of circle
Let the center of the circle (a, 2a) be set, and the chord center distance D can be obtained from the chord length formula=
10−8=
2，
From the distance formula of point to line, d = | a − 2A|
2=
Two
2|a|，
The center coordinate of the circle is (2,4), or (- 2, - 4), and the radius is
10，
The equation of the circle is: (X-2) 2 + (y-4) 2 = 10 or (x + 2) 2 + (y + 4) 2 = 10
In circle O, if the radius is 5 and the length of a chord is 8, what is the distance from the center of the circle to the chord? What is the distance from the midpoint of the arc to the chord?
3. Chord length, the line from the center of the circle to the midpoint of the chord (i.e. the distance required) can form a right triangle of 3.4.5
2. This is the radius minus the distance from the midpoint of the arc to the chord
I don't know how to write the process. I can see it
If there are two parallel chords in a circle with a radius of 5cm, one is 8cm long and the other is 6cm long, then the distance between the two chords is______ Centimeter
As shown in the figure, CD = 8, ab = 6, OA = OC = 5, ab ∥ CD, of ⊥ AB, OE ⊥ CD,
According to the vertical diameter theorem, point E is the midpoint of CD, CE = 4cm, point F is the midpoint of AB, AF = 3cm,
According to Pythagorean theorem, OE=
OC2−CE2=3cm，OF=
OA2−AF2=4cm，
There are two cases,
① When the chord AB and string CD are on the same side of the circle center, the distance between string AB and string CD is EF = of-oe = 4-3 = 1cm,
② When the chord AB and string CD are on the opposite side of the circle center, the distance between chord AB and string CD is EF = of + OE = 4 + 3 = 7cm
Therefore, the distance between the strings is 1cm or 7cm
Given that the radius of the circle is 5 and the distance from the center of the circle to the chord is 4, then the chord length is?
Given that the radius of the circle is r = 5 and the distance from the center of the circle to the chord is p = 4, then the chord length L is?
L=2*(R^2-p^2)^0.5
=2*(5^2-4^2)^0.5
=6
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