The linear equation passing through point a (1,2) and the maximum distance from the origin is______ .

. according to the meaning of the question, when it is perpendicular to the straight line OA, the distance is the largest,
Since the slope of the line OA is 2, the slope of the straight line is − 1
2，
Therefore, from the point oblique equation: y − 2 = − 1
2(x−1)，
The result is: x + 2y-5 = 0,
So the answer is: x + 2y-5 = 0

The equation of the straight line passing through the origin and the same distance from two fixed points a (- 1,1), B (3, - 2)

Cross origin
So kx-y = 0
The distance is equal
So | - k-1 | / √ (K | + 1) = | 3K + 2 | / √ (K | + 1)
|k+1|=|3k+2|
k+1=±(3k+2)
k=-1/2,k=-3/4
So x + 2Y = 0 and 3x + 4Y = 0

The set of points whose distance from the space to the fixed point a (- 1,0,4) is equal to 3 is? The equation is? Hope there is a process,

The set of points is a sphere with point a (- 1,0,4) as its center and 3 as its radius. The equation is (x + 1) ^ 2 + y ^ 2 + (Z-4) ^ 2 = 0

The graph of the set whose distance from the space to the fixed point (- 1,0,4) is 3, and its equation is?

The equation is (x + 1) 2 + y 2 + (Z-4) 2 = 9

The set of points whose distance from a fixed point is equal to a fixed length is

It means a circle. The distance from all the points on the circle to the center of the circle is equal to the radius! The fixed point is the center of the circle, and the fixed length is the radius! This is the method of using set to express the circle in high school mathematics

It is known that the ratio of distance from point P (2, - 5), two points a (3, - 2), B (0,6) to line L is 1:2, and the equation of line L is obtained

(1) If the slope of the straight line does not exist, then the linear equation is: x = 2
At this time, the distance from a to the straight line D1 = 1, and the distance from B to the straight line D2 = 2, which meets the meaning of the question;
(2) If the slope is k, then the linear equation is: y + 5 = K (X-2), that is: kx-y-2k-5 = 0
The formula of distance from point to line, the distance from a to line D1 = | K-3 | / √ (k? + 1)
The distance from B to the straight line D2 = | - 2k-11| / √ (k? + 1)
From the meaning of the title: D1 / D2 = 1 / 2
That is, | K-3 | / | - 2k-11 | = 1 / 2
|2k-6|=|-2k-11|
2k-6 = - 2k-11 or 2k-6 = 2K + 11
No solution
So, k = - 5 / 4
Therefore, the equation of the line L is: y + 5 = - 5 (X-2) / 4, that is, 5x + 4Y + 10 = 0
To sum up, the equation of the line L is: x = 2 or 5x + 4Y + 10 = 0
Wish you happy! Hope to help you, if you do not understand, please ask, I wish you progress_ ∩)O

It is known that the straight line L passes through the point (5,10) and the distance between it and the origin is 5. Find the equation of the straight line L

Equation y - 10 = K (x - 5) of line L
kx - y + 10 - 5k = 0
The distance from the origin d = | k * 0 - 0 + 10 - 5K | / √ (k? + 1) = 5| K - 2 | / √ (k? 2 + 1) = 5
k = 3/4
y - 10 = (3/4)(x - 5)
y = 3x/4 - 25/4

Find the equation of the straight line passing through the point P (- 3,4) and the distance from the origin is equal to 5

Y = 3 (x + 3) / 4 + 4, that is 3x-4y + 25 = 0

Of all the lines passing through point m (3,5), what is the equation of the line farthest from the origin?

The line passing through M and farthest from the origin is perpendicular to OM,
From Kom = 5 / 3, the slope of the straight line is k = - 1 / Kom = - 3 / 5,
So the equation is Y-5 = - 3 / 5 * (x-3),
3 x + 5 y - 34 = 0

In the straight line passing through point a (- 3,1), the equation of the line farthest from the origin is______ .

If the origin is O, then the straight line passing through point a (- 3,1) and perpendicular to OA, and then koa = - 1
3，
The slope of the line is 3,
The equation is Y-1 = 3 (x + 3), that is 3x-y + 10 = 0
So the answer is: 3x-y + 10 = 0

The linear equation passing through point a (1,2) and the maximum distance from the origin is______ .