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What is the equation for all lines passing through the point (- 3,1) and the line farthest from the origin
The farthest line is the line perpendicular to (-3,1) (called A) and the origin o
The X-Y axis is on PQ
Draw a picture and make AB perpendicular to the X axis, ab = 1, Bo = 3,
So the photography theorem (if you haven't learned it, you can prove the similarity)
Pb * Bo = the square of Ba
PB=1/3,PO=10/3
P（-10/3,0）
Re triangle PBA is similar to triangle poq
OQ/AB=PO/PB=10
OQ=10
Q（0,10）
Then put the coordinates into a function of order one
y=kx+b
b=10
-10k/3=-10
K=3
Analytic formula y = 3x + 10
If it's not vertical, you can do whatever you want, and then about the distance of O, that is, the vertical line, you can draw this conclusion by using the hypotenuse of a right triangle greater than the right side
Of all the lines passing through point a (- 3,2), what is the equation of the line farthest from the origin
Set the origin o, so the farthest distance from the origin to the straight line is OA, and OA is perpendicular to the line
The slope of OA is (2-0) / (- 3-0) = - 2 / 3
Let the linear equation be y = KX + B
Then the slope of the line is k = - 1 / (- 2 / 3) = 3 / 2
Straight line again (- 3,2)
b=9/2
So the linear equation is y = 3 / 2x + 9 / 2
In all kinds of straight lines passing through point a (- 3,2), what is the linear equation farthest from the origin?
Among all the lines passing through point a (- 3,2), if the farthest distance from the origin is equal to OA, then the line is perpendicular to OA;
If the slope of OA is - 2 / 3, the slope of the straight line perpendicular to OA is 3 / 2;
It can be assumed that the equation of the straight line is y = (3 / 2) (x + b), and the line passes through the point a (- 3,2),
2 = (3 / 2) (- 3 + b), B = 13 / 3;
Therefore, among all the lines passing through point a (- 3,2), the equation of the line farthest from the origin is as follows:
y = (3/2)(x+13/3) =(3/2)x+13/2 .
Given the point P (2, - 1) (1), the equation of the straight line passing through the point P and the distance from the origin is 2; (2) What is the maximum distance of the equation for the line passing through the point P and having the largest distance from the origin?
(1) Let the equation a (X-2) + B (y + 1) = 0,
The distance from the origin to the straight line is | a (0-2) + B (0 + 1) | / √ (a ^ 2 + B ^ 2) = 2,
B (3b + 4a) = 0,
If a = 1, B = 0 or a = 3, B = - 4, the linear equation is X-2 = 0 or 3x-4y-10 = 0
(2) When the distance from the origin to the straight line is maximum, Op L,
From KP = - 1 / 2, KL = 2, so the linear equation is y + 1 = 2 (X-2), which is converted into 2x-y-5 = 0,
The maximum distance is | op | = √ [(0-2) ^ 2 + (0 + 1) ^ 2] = √ 5
If a straight line is parallel to y = x + 5 and the distance from the origin is 2, then the equation of the line is
y=x±√2
Given the point P (2,1), find the equation of the straight line with the largest distance from the origin
You can draw a picture, the origin is O, draw a straight line randomly through point P, make the vertical line from point O to line, and set the intersection point as a. because in the right triangle Pao, the oblique side Po is always greater than Ao, so only when point a and point P coincide, that is, Po is perpendicular to the straight line, the distance between the origin and the line is the largest
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 (- 4,3) and the distance from the origin is equal to 5 is A 3X-4Y+25=0 B 4X-3Y-25=0 C 4X+3Y+25=0 D 4X-3Y+25=0
D
Bring in a, only D passes through point a
What is the equation of the line passing through the point (- 4,3) and the distance from the origin is equal to 3?
Point oblique equation
y-3=k(x+4)
Turn it into a general formula
kx-y+4k+3=0
Formula of distance from point to line
|4K + 3 | / root sign (k square + 1) = 3
K = 0 or K = 24 / 7
In a circle of radius 1, the degree of the circular angle to which the chord of length 1 is opposite?
30 degrees
Connect the two ends of the chord to the center of the circle. Because the radius is 1 and the chord is 1, there is an equilateral triangle. Therefore, the center angle of the chord is 60 ° and the circumferential angle is 60 ° and 30 ° respectively
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