If the radius of two circles is 3 and 4, and the distance between centers is 7, then the position relationship between the two circles is () A. Separation B. Exotomy C. Endonuclease D. Intersection

∵ the radii of the two circles are 3 and 4 respectively, and the center distance is 7,
∴3+4=7，
The position relationship between the two circles is circumscribed,
Therefore, B

Given the circle with the origin as the center and radius of 5, find the relationship between the vertex and the circle of the quadratic function y = xsquare-6x + 13

The analytic expression of this quadratic function can be transformed into
y=(x-3) ²;+4,
That is to say, this is a parabola, the opening is upward, and the vertex coordinates are (3,4)
The distance between the point and the origin = under the root sign (3? 2 + 4? 2) = 5
The visible vertex is on the circle

It is known that the center of a circle is the origin of coordinates and its radius is 2. From any point P on the circle, a perpendicular line is drawn to the X axis, and the perpendicular foot is p

The center of a circle is the coordinate origin and the radius is 2. The equation of this circle is x + y = 2 (1)
If a vertical line Pb is made from any point on the circle to the x-axis, then the midpoint 2 * Y1 = y of the line Pb is substituted into (1)
Its trajectory is an ellipse whose major axis (on the X axis) is 2 and the minor axis (on the Y axis) is 1

As shown in the figure, P (x, y) is the point on the circumference with the coordinate origin as the center and 5 as the radius. If x and y are integers, then such points are common______ One

∵ P (x, y) is the point on the circle with the coordinate origin as the center and 5 as the radius,
That is, the distance from any point on the circle to the origin is 5,
According to the meaning of the title:
In other words, YX2 + 2 = 25,
And ∵ X and y are integers,
The integer solutions of the equation are: x = 0, y = 5; X = 3, y = 4; X = 4, y = 3;
x=5，y=0；x=-3，y=4；x=-4，y=3；
x=-5，y=0；x=-3，y=-4；x=-4，y=-3；
x=0，y=-5；x=3，y=-4；x=4，y=-3．
There are 12 pairs, so there are 12 coordinates
They are: (0, 5); (3, 4); (4, 3); (5, 0); (- 3, 4); (- 4, 3); (- 5, 0); (- 3, - 4); (- 4, - 3); (0, - 5); (3, - 4); (4, - 3)

The center of a circle is known to be the origin of coordinates and the radius is 2 (1). From any point P on the circle, make the vertical line PP ', and find the locus of the midpoint m of the line PP' (2) Let n (x, y) be any point of the trajectory in (1), and find the value range of u = 2x + 3Y The first question is known, x 2 + 4Y 2 = 4, ask the second question

(2) ∵ n (x, y) on the ellipse ᙽ u = 2x + 3Y and X? + 4Y? = 4 have a common point y = (u-2x) / 3 substituting x? + 4Y? = 4x? + 4 [(u-2x) / 3]? = 4 finishing: 9x? + 4 (U? - 4ux + 4x? - 36 = 025x? - 16ux + 4U? - 36 = 0 ᙨ Δ = 256u

The point P (x, y) is a point on the circle where the origin of the coordinate is the center of the circle and 5 is the radius. If x and y are integers, then such points have common () A. 4 B. 8 C. 12 D. 16

12
0,5 0,-5 5,0 -5,0
3,4 -3,4 3,-4 -3,-4
4,3 -4,3 4,-3 -4,-3

In the plane rectangular coordinate system, 0 is the coordinate origin, and the circle with 0 as its center is tangent to the straight line x-radical 3y-4 = 0 In the plane rectangular coordinate system, 0 is the coordinate origin, and the circle with 0 as its center is tangent to the straight line x-radical 3y-4 = 0 Find circle 0 equation

The radius of a circle is the distance from the center of the circle to the straight line,
So according to the formula, r = 4 / radical (1 + 3) = 2
The formula is the absolute value / root sign of D = (AX 2 + by 2 + C) of the distance from a point to a straight line
So the equation for a circle is x? 2 + y? 2 = 4

In the plane rectangular coordinate system, O is the origin. If a (radical 3, - 1) is rotated 270 ° around o to point B, then the coordinate of point B is

The angle between the connecting line of this point and the far point and the negative half axis of X axis is 30 degrees. After 270 degrees rotation, it should be 60 degrees with the positive direction of X axis. The coordinate of the necessary point should be (1, negative root sign 3)

In the plane rectangular coordinate system, O is the coordinate origin, the coordinate of vertex a of rectangular trapezoid ABCD is (0, root 3) and the coordinate of point D is (1, root 3) Point C is on the positive half axis of x-axis, and the parabola passing through point O and taking point D as its vertex passes through point C, and point P is the point on line CD (not coincident with CD). The straight line OP divides the trapezoidal AOCD area into two parts: 2:1. Find out the parabola 1 · line analytic formula to find whether there is Q on the parabola on the right side of y-axis, so that the circle with Q as the center is tangent to Y-axis and line OP at the same time, Write out the point P coordinate point m is a moving point on the line segment op (not coincident with O), the circle passing through the point OMD intersects with the positive half axis of Y axis at point N.M. in the process of motion, the value of OM + on will not change? If not, ask for this value. If it changes, please write out the change range

(1) According to the meaning of the question, let the analytic formula of parabola be y = a (x-1) ^ 2 + radical 3, and substitute o (0,0) into the solution to obtain a = - radical 3, so the analytic formula of parabola is y = (- radical 3) (x-1) ^ 2 + radical 3;
(2) The coordinate of point C is (2,0), and the analytic formula of CD can be obtained as y = (- radical 3) x + 2 radical 3. According to the meaning of the question, the ordinate of point P is (root 3) / 2. Substituting the analytic formula of CD, we can get x = 3 / 2, that is, the coordinate of point P is [3 / 2, (root 3) / 2];
(3) There is a point Q on the parabola on the right side of the y-axis, so that the circle with the point Q as the center is tangent to the Y-axis and the straight line OP at the same time. The coordinates of the point q are (m, n). If the y-axis is perpendicular to the y-axis, and the op perpendicular intersects OP at the f-point, then QE = QF = m, and the equation of the straight line OP can be obtained as (radical 3) x-3y = 0, so QF = I (radical 3) m-3n = 2 (radical 3) m, then i7-3mi = 2, M = 5 / 3,
N = (5 root sign 3) / 9 or M = 3, n = - 3 root sign 3, that is, the coordinate of point q is (5 / 3, (5 root sign 3) / 9) or (3, - 3 root sign 3);
(4) The analytic formula of OP is y = x / radical 3, the coordinates of point m are (m, M / √ 3), and the equation of circle passing through points o, m and D is as follows:
X 2 + y 2 + DX + ey = 0, substituting the coordinates of point D and m into the
D + √ 3E + 4 = 0,3md + √ 3me + 4m2 = 0, the solution d = 2-2m, e = (2m-6) / √ 3
The equation of ⊙ q is x ⊙ y ⊙ 2 ᙽ 2 ᙽ 2 ⊙ 2 ᙽ 2 ᙽ 2 ᙽ 2

In the plane rectangular coordinate system, O is the coordinate origin, the coordinates of vertex a of right angled trapezoid AOCD are (0, root 3), and the coordinates of point D are (1, root 3), Point C is on the positive half axis of x-axis, and the parabola passing through point O and taking point D as its vertex passes through point C. point P is a moving point on line CD (not coincident with points c and D), and the straight line OP divides the area of AOCD into two parts: 2:1 (1) Solving the analytic formula of parabola (2) Find the coordinates of point P (3) Whether there is a point Q on the parabola on the right side of the y-axis, so that the circle with the center of the point q is tangent to the Y-axis and the straight line op. if there is, ask for the coordinates of the point Q satisfying the conditions; if not, please explain the reasons (4) Point m is the moving point on line op (not coincident with point o). The circle passing through point O, m and D intersects with the positive half axis of Y axis at point n. M. in the process of motion, is the value of OM + on unchanged? If not, ask for this value; if it changes, please write out the range of change directly Mainly (4), (4) Point m is a moving point on line op (not coincident with point o). The circle passing through point O, m and D intersects with the positive half axis of Y axis at point n. M. in the process of motion, is the value of OM + on unchanged? If not, ask for this value; if it changes, write down the change range directly

If the radius of two circles is 3 and 4, and the distance between centers is 7, then the position relationship between the two circles is () A. Separation B. Exotomy C. Endonuclease D. Intersection