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Two points a (1, 6) are known 3)，B(0，5 3) If the distance to the straight line L is equal to a, and such a line l can be made into four lines, then the value range of a is______ .
∵ if a and B are on the same side of the line L, two straight lines can be made,
If such a line l can be made into four lines, then when two points a and B are on both sides of the line L, there should be two more
ν 2a is less than the distance between a and B
∵|AB|=
(1−0)2+(6
3−5
3)2=2
∴0＜2a＜2，∴0＜a＜1
So the answer is 0 < a < 1
A straight line passes through point a (2, - 3) and its slope is equal to 2 times of the slope of the line y = 1 / root sign 3 times X
Y = 1 / √ 3 x has a slope of 1 / √ 3
So the slope of the line is 2 / √ 3 = 2 √ 3 / 3
So y - (- 3) = (2 √ 3 / 3) (X-2)
2√3x-3y-4√3-9=0
The distance between a (6,5) B (- 2,3) two points and the line L is equal, and the equation of line L is solved,
The distance between a (6,5) B (- 2,3) two points and the line L is equal
Then the line AB is parallel to the line to be calculated or a and B are symmetric about the line
When parallel
Kab=(5-3)/(6+2)=2/8=1/4
So the linear equation is y = x / 4
When symmetric
xa=(6-2)/2=2 ya=(5+3)/2=4
Substituting the linear equation y = kx
4=2k
K=2
So the linear equation is y = 2x
Given that the straight line L passes through the point P (5,10) and the distance from the origin to it is 5, then the equation of the line L is______ .
When the slope of the line does not exist, the equation of the line is x = 5, which satisfies the condition. When the slope of the line exists, let the equation of the line be Y-10 = K (X-5), that is, kx-y-5k + 10 = 0. From the condition, − 5K + 10 | 1 + K2 = 5, | k = 34, so the equation of line is 3x-4y + 25 = 0
The intercept of the line L on the Y axis is 10, and the distance from the origin to the straight line is 8
If the intercept of the line L on the y-axis is 10, the equation of the oblique section of the line is y = KX + 10, that is, kx-y + 10 = 0, and the distance from the origin to the straight line is 8 | | 0 × k-0 + 10 | / √ (1 + k ^ 2) = 8, that is, 10 / √ (1 + K ^ 2) = 8 (1 + K ^ 2) = 10 / 8 = 5 / 4. The equation of line L is y = (3 / 4) x + 10 or y = - (3 / 4)
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______ .
When the slope of the straight line does not exist, the equation is x = - 2
When the slope of the line exists, let the equation of the line be Y-3 = K (x + 2), that is, kx-y + 2K + 3 = 0,
2 = | 0 − 0 + 2K + 3|
k2+1，∴k=-5
So the equation of the line L is x = - 2, or 5x + 12y-26 = 0
To sum up, the equation of the line L satisfying the condition is x = - 2, or 5x + 12y-26 = 0,
So the answer is x = - 2, or 5x + 12y-26 = 0
A (2,3), B (- 4,8) two points, the straight line L passes through the origin, and the distance between the two points a and B to the straight line L is equal, find the equation of the straight line L RT
y=kx
kx-y=0
A. The distance between L and two points of the line is equal,
|2k-3 | / root sign (k ^ 2 + 1) = | - 4k-8 | / root sign (k ^ 2 + 1)
|2k-3|=|4k+8|
2k-3 = 4K + 8 or 2k-3 = - 4k-8
k=11/2,k=-5/6
y=11x/2,y=-5x/6
The set of points whose distance from the space to the fixed point a (- 1,0,4) is equal to 3 is? Its equation is?
A sphere whose center is at point a and whose radius is 3
(x+1)^2+y^2+(z-4)^2=9
Given that the distance between the straight line L and two points a (4,3), B (- 4, - 3) is equal to 3, find the equation of the straight line L
In two cases, there are four straight lines in accordance with the meaning of the title: 1 and ab are parallel, let L: 3x-4y + C = 0 (slope is 3 / 4) AB: y = (3 / 4) x, that is 3x-4y = 0, so | c-0 | - = 3 √ 3? + 4? C = ± 15, so l: 3x-4y + 15 = 0 or 3x-4y-15 = 0; ②: l passes through the midpoint of AB (i.e., the origin) and l: 3x-4y-15 = 0
If the straight line L passes through the point (5.10) and the distance from the origin is equal to 5, find the equation of L;
Let the linear equation y = KX + B
10=5K+B
The distance to the origin is five, so
B / root sign (1 + K ^ 2) = 5
K = 12 / 5, B = - 2
So the equation is y = 12x / 5-2
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