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The straight line L passes through the origin, and the distance between the point m (5,0) and the line L is equal to 3
Let y = KX, according to the formula of the distance from the point to the straight line, k| can be obtained by dividing the following sign, k = plus or minus 3 / 4
The equation of the straight line passing through the point P (- 4,3) and the distance from the origin is equal to 5
Through the point P, let the equation be y = K (x + 4) + 3, that is, y-kx-4k-3 = 0
The distance from the origin is substituted into the formula i4k-3 Ⅰ / √ (k ^ 2 + 1) = 5
K = - 4 / 3, so l: 3Y + 4x + 7 = 0
Of all the lines passing through point m (3,5), what is the equation of the line farthest from the origin?
The straight line passing through the point m (3,5) and perpendicular to OM is the line to be calculated, and the slope k ′ = 5 − 0
3−0=5
3，
Then the slope of the straight line k = - 3
5，
The equation of the straight line is Y-5 = - 3
5（x-3）
The result is: 3x + 5y-34 = 0
What is the equation of the line passing through the origin and the distance from point a (2,1) equal to 1?
Because it goes through the origin
When the slope k exists
Let K y = X,
That is, kx-y = 0
And the distance to point a (2,1) is equal to 1
In other words, d = | 2k-1| / root sign [K + (- 1) 2] = 1
Sort it out as
3k²+4k=0
That is, K (3K + 4) = 0
K = 0 or K = 0
That is, the straight line is
Y = 0, or y = - 4x / 3
Or not quite
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 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
Find the equation of the straight line L passing through the point P (- 4,3) and the distance from the origin is equal to 4 Complete the steps of solving the problem
Let the linear equation passing through point p be
y-3=k(x+4)
kx-y+4k+3=0
So the distance from the origin d = | 4K + 3 | / √ (k ^ 2 + 1) = 4
Simplified
24k=-5
k=-5/24
So the linear equation is
y-3=-5/24(x+4)
y=-5x/24+13/6
Find the linear equation passing through the point (- 4,3) and the distance from the origin is equal to 5
The distance from the point (- 4,3) to the origin is 5
From this we can get that the line from the point (- 4,3) to the origin is perpendicular to the line
Then their slopes are negative reciprocal of each other
The slope of the line from point (- 4,3) to origin is - 3 / 4
So the required slope of the line is 4 / 3
Using the point oblique formula Y-3 = 4 / 3 (x + 4) in the linear equation
The result shows that 4x-3y + 25 = 0
Find the equation of two parallel lines passing through the origin and point a (1,3) respectively and the distance is equal to the root 5 We need the process,
Let the slope K
Then the two parallel line equations are as follows:
y=kx => kx-y=0
y-3=k(x-1) => kx-y+(3-k)=0
Radical 5 = |3-k| / (k ^ 2 + 1) ^ (1 / 2)
5(k^2+1)=(3-k)^2
2k^2+3k-2=0
(2k-1)(k+2)=0
K = 1 / 2 or K = 2
So, two parallel line equations:
Y = (1 / 2) x and y = (1 / 2) x + (5 / 2)
Or: y = - 2x and y = - 2x + 5
It is known that the base length of an isosceles triangle is 8 and the waist length is a root of the equation x2-9x + 20 = 0
As shown in the figure below:
∵x2-9x+20=0，
（x-4）（x-5）=0，
∴x1=4，x2=5；
The base length of isosceles triangle is 8,
When x = 4, the three line segments of 4, 4, 8 cannot form a triangle,
Therefore, the waist length is x = 5,
Let the height be h, and from Pythagorean theorem we can get the following results
H=
52−42=3，
The height is 3,
So, the area of the triangle is 1
2×8×3=12．
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