Given that the intersection of (x-3) 2 + y2 = 4 and the line y = KX passing through the origin is p, Q, then the absolute value of OP is multiplied by the absolute value of OQ

Simultaneous equations (x1, Y1) (X2, Y2)
Results = (under root sign (x1 square + Y1 Square)) * (under root sign (x2 square + Y2 Square))

If the line passing through point (2,1) intersects with circle x ^ 2 + y ^ 2 = 9 at two points a and B, then the minimum value of the module to AB is

Because 2 ^ 2 + 1 ^ 2

What is the minimum value of | ab | if the line passing through point P (1,5) intersects with circle x ^ 2 + y ^ 2-4x-9y + 4 = 0 at two points a and B

The circular equation can be written as (X-2) ^ 2 + (Y-3) ^ 2 = 3 ^ 2
The center of the circle C is (2,3) and the radius is 3
According to the graph, when CP bisects AB vertically, AB is the shortest
CP=√(2-1)^2+(3-5)^2=√5
There is Pythagorean theorem, AB / 2 = √ 3 ^ 2-5 = 2
AB=4

Given the point P (1,2) and the circle C: X & # 178; + Y & # 178; = 251), if the line y = x + B intersects the circle C at two points a and B, find the trajectory equation of the midpoint m in ab

Because there are two intersections between the line and the circle, the position relationship between the line and the circle is intersection. At this time, the midpoint m of AB must satisfy that CM is perpendicular to AB, and the known slope of AB is fixed to 1, so the slope of CM is fixed to - 1
Therefore, it can be intuitively judged that the trajectory of point m is the part of the straight line passing through point C with a slope of - 1 in the circle (excluding the intersection point),
The specific equation is y = - x, - 5

Among all the lines crossing point P (0,1) and circle x2 + y2-2x-3 = 0, the linear equation of the longest chord cut by circle is ()
A. x=0B. y=1C. x+y-1=0D. x-y+1=0

It is easy to know that the diameter of the circle is in line with the meaning of the topic. Since the center of the circle is O (1,0) and passes through the point P (0,1), the slope of the straight line k = 1 − 00 − 1 = − 1, then according to the point oblique equation Y-1 = - 1 (x-0), that is, x + Y-1 = 0, so C

Find the linear equation of point P (5,5) and circle x ^ 2 + y ^ 2 = 25, chord length is 4 times root sign 5
It is inconvenient to use 4 {5} to represent 4 times root 5

The radius of the circle C: x ^ 2 + y ^ 2 = 25 is r = 5
According to the Pythagorean theorem, the distance from the center of circle to the straight line L is: D ^ 2 = R ^ 2 - (2 radical 5) ^ 2 = 25-20 = 5
D = root 5
Let the linear equation be Y-5 = K (X-5)
That is: kx-y + 5-5k = 0
D = | 5-5k | / radical (k ^ 2 + 1) = radical 5
(5-5k)^2=(k^2+1)*5
25-50k+25k^2=5k^2+5
20k^2-50k+20=0
4k^2-10k+4=0
(4k-2)(k-2)=0
K = 1 / 2 or K = 2
The equation is: 2x-y-5 = 0 or 1 / 2x-y + 5 / 2 = 0

What is the arithmetic square root of 13

Positive root 13

arithmetic square root

1,1.414.1.732,2,2.236,2.449,2.646

If the square roots of A-B + 1 and a + 2B + 4 are opposite to each other, what is the power of (a + b) to 2004?
Urgent, children's shoes all help. Thank you
Yes, the title is wrong. Thank you for reminding. It should be (a-b)

The square roots of A-B + 1 and a + 2B + 4 are opposite to each other
The square root of A-B + 1 + A + 2B + 4 = 0
∴ a-b+1 = 0
a+2b+4 = 0
∴ a = -2
b = -1
2004 power of (- 2-1)
=The power of (- 3)
=The power of 3
The first floor is right
The title must be wrong

Given that the intersection of (x-3) 2 + y2 = 4 and the line y = KX passing through the origin is p, Q, then the absolute value of OP is multiplied by the absolute value of OQ