Line L and circle x ^ 2 + y ^ 2 + 2x-4y + a = 0 (a)

(x + 1) ^ 2 + (Y-2) ^ 2 = 5-a center O (- 1,2) let (0,1) be C, because C is the midpoint of AB, so OC vertical aboc slope = (2-1) / (- 1-0) = - 1, so AB slope = 1, over (0,1) so Y-1 = 1 * (x-0) X-Y + 1 = 0

As shown in the figure, two straight lines L1 and L2 in the plane intersect at point O. for any point m in the plane, if P and Q are the distances from m to line L1 and L2 respectively, then the ordered nonnegative real number pair (P, q) is called the "distance coordinate" of point M. according to the above definition, the number of points whose "distance coordinate" is (1,2) is______ ．

As shown in the figure, two lines L1 and L2 in the plane intersect at point O. for any point m in the plane, if P and Q are the distances from m to line L1 and L2 respectively, then the ordered nonnegative real number pair (P, q) is called the "distance coordinate" of point M. according to the above definition, the point whose "distance coordinate" is (1,2) can be found in each of the four regions formed by the intersection of two lines, so the condition is satisfied So the answer is: 4

The circle C (x-1) 2 + (Y-3) 2 = 4, the line L passing through the origin o intersects the circle C at two points AB, if the chord length of AB is 2, the root sign is 2, the sphere is directly limited to L
equation

Circle C (x-1) 2 + (Y-3) 2 = 4
Center C (1,3), radius r = 2
If l passes through the origin, the slope must exist. Let l be K
The equation is y = KX, that is kx-y = 0
A straight line L is cut by a circle C to obtain a chord AB with a chord length of 2 √ 2,
So the distance between the center of the circle C and the line l
d=√(r²-2)=√2
According to the distance formula from point to line:
d=|k-3|/√(k^2+1)=√2
∴(k-3)^2=2(k^2+1)
That is, K ^ 2 + 6k-7 = 0
The solution is k = 1 or K = - 7
The equation of line L is
Y = x or y = - 7x

As shown in the figure, in the plane rectangular coordinate system, there are several integer points, whose order is arranged in the direction of "→", such as (1,0), (2,0), (2,1), (3,2), (3,1), (3,0) According to this rule, the coordinates of the 100th point are______ ．

It can be seen from the graph that the number of points is 1, 2, 3, 4, 5 When the abscissa is even, the arrow is upward, ∵ 1 + 2 + 3 + +13=91，1+2+3+… +14 = 105, the coordinates of the 91st point are (13, 0), the abscissa of the 100th point is 14. ∵ the direction of the point on the 14th line is upward, and the ordinate is from the 92th to the 92th

If the midpoint C of chord AB is (- 2,3), then the equation of line L is ()
A. x-y+5=0B. x+y-1=0C. x-y-5=0D. x+y-3=0

From the general equation of the circle, we can get the center O (- 1,2). From the properties of the circle, we can easily know that the line of O (- 1,2), C (- 2,3) is perpendicular to the string AB, so there is kabkoc = - 1 ﹥ KAB = 1, so the equation of the straight line AB is: Y-3 = x + 2, sorted out: X-Y + 5 = 0, so we choose a

Which direction is the x-direction coordinate and which direction is the y-direction coordinate in the building general plan?

The north and South are x and the East and West are y

It is known that the line L passing through the point m (- 3, - 3) intersects the circle x ^ 2 + y ^ 2 + 4y-21 = 0 at two points a and B. let the midpoint of the chord AB be p, and the trajectory equation of the moving point p be obtained

In fact, the trajectory equation is to find out an equation relation with X and y of the point!
Here you can. Here you are
1. When K (slope) exists, let p be (x, y). Then, there is a slope between P and the center of the circle
2. The line between P and M is a slope
3, use the product of two K is equal to - 1, then simplify!
4, please continue to explore the situation that K does not exist!

The cinema is 3 kilometers away from the shopping mall. On the 500 meter plan, what is the distance between the two buildings?

3000/500=6(cm)

Take a random number x in the interval [- π 2, π 2]. The probability that the value of cosx is between 0 and 12 is ()
A. 13B. π2C. 12D. 23

The interval length of all basic events is π 2 − (− π 2) = π∵0 ≤ cos x ≤ 12. The solution of π 3 ≤ x ≤ π 2 or − π 2 ≤ x ≤ − π 3 ℅ "cos & nbsp; X values between 0 and 12" contains the interval length of π 3. According to the geometric probability formula, the probability of COS & nbsp; X values between 0 and 12 is p = π 3, π = 13, so select a

Calculate (double integral) XY ^ 2dydz + YZ ^ 2dzdx + ZX ^ 2dxdy in the range of the upper side of the upper hemisphere z = root 1-x ^ 2-y ^ 2

Let P = XY \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\dzdx + ZX &

Line L and circle x ^ 2 + y ^ 2 + 2x-4y + a = 0 (a)