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It is known that in the plane rectangular coordinate system, point P is in the third quadrant, the circle P is tangent to the x-axis, is tangent to the point Q, and intersects the y-axis with m (0, - 3) n（
If you haven't said all of your questions, I'll tell you the idea. Connect OP, do pH ⊥ Mn to get rectangle oqphop = Oh OQ = hpoh. You can calculate by yourself, Mn = NH = half Mn. Then Oh is obtained by subtracting Mn from on, so OP is also obtained, so its axis coordinates have horizontal coordinates, you connect PM first, so PM = OP, because
In the plane rectangular coordinate system, point O is the coordinate origin, the quadrilateral ABCO is rhomboid, the coordinate of point a is (- 3,4), and the coordinate of point a is (- 3,4) Point C is on the positive half axis of the X axis, the line AC intersects the Y axis at point m, and the edge AB intersects the Y axis at point H (1) Whether there is a P point on AC to minimize the circumference of △ PBH. If so, request the minimum value of this p point and the circumference of △ PBH. If not, please explain the reason (2) Connect BM, as shown in Figure 2. Starting from point a, the moving point Q moves uniformly to the end point C at a speed of 2 units / s along the broken line ABC direction. Let the area of △ QMB be s (s ≠ 0) and the movement time of point Q be T seconds, then find the functional relationship between S and t (the value range of independent variable t should be written out)
It is easy to get: ① a (- 3,4) B (2,4) C (5,0) ② AB = BC = co = OA = 5. ③ the analytic formula of the straight line AC is: y = - 1 / 2 x + 5 / 2 ④ H (0,4) m (0,5 / 2) ⑤ AC = 4 √ 5 (1). It is obvious that there is a point P that meets the conditions. The point P is the one that meets the conditions
As shown in the figure, in the plane rectangular coordinate system, the quadrilateral ABCO is a diamond, and ∠ AOC = 60 ° The coordinate of point B is (0,8 √ 3). Starting from C, point P moves on line CB at the speed of 1 unit length per second to point B. at the same time, point Q starts from point O and moves along the direction of ray OA at the speed of a (1 "a" 3) unit length per second
Confirm the following points:
1. The coordinate of B is (0,8 √ 3), and point B is on the Y axis
2. A (1 "a" 3) whether a (1 ≤ a ≤ 3)
3. T (0bp, the intersection point of QP and ob is on the extension line of OB direction
∵OB＝8√3＞4√3／3＝OD
The intersection point of QP and ob is on the extension line of OB direction
3. When t
In the plane rectangular coordinate system, O is the origin coordinate, and the parabola y = 1 / 2x 2 + 2x intersects the X axis at O B two points, and the vertex is a connecting OA If you shift the parabola y = 1 / 2x 2 + 2x 4 units to the right and 2 units down
Well, it's your third year in junior high school. So am I
In fact, you only need to convert it into vertex form, and then get a new vertex form by moving the vertex
Answer: y = 1 / 2 (X-2) 2 - 4
In the plane rectangular coordinate system, the coordinate of point a is [6,0]. Point P is on the straight line y = - x + m, and AP = OP = 5. Find the value of M
AOP is an isosceles triangle. The distance between P and X axis is equal to 4 (the Pythagorean theorem of right triangle 345). M is equal to the value of the linear equation when x is equal to 0. According to the central line principle, it should be equal to 8
In the plane rectangular coordinate system, the vertex o of the rhombus oabc is at the origin, the vertex B is on the positive half axis of the Y axis, and the OA edge is at the y = root of the straight line In the plane rectangular coordinate system, the vertex O of diamond OABC is at the origin, the vertex B is on the positive half axis of Y axis, the edge OA is on the line y= root 3x, and the edge AB is on the line y= negative root 3x+ root 3. Then the coordinates of the vertices O and C are in turn? What is the side length OA of the diamond? What is the degree of a?
The intersection point of the straight line OA and ab is the coordinate of point a, the intersection point of AB and Y axis is the coordinate of point B, and the intersection point of AB and Y axis is (0, √ 3). The two straight lines are combined to obtain the intersection point as (0.5,0.5 √ 3), i.e. a coordinate. Since it is rhombus, AC points are symmetrical about y axis, then C coordinate is (- 0.5, 0.5 √ 3)
As shown in the figure, the vertex o of lozenge oabc is at the coordinate origin, and vertex A is on the X axis, ∠ B = 120 ° and OA = 2. Rotate the rhombic oabc clockwise about the origin by 105 ° to the position of oa'b'c ', then the coordinates of point B' are
Connect ob, ∵ oabc is a diamond, ? OA = AB, ? ABC = 120 degrees, ? OAB = 60 degrees, ? OAB is an equilateral triangle, ? ob = OA = 2, ∵ AOB = 60 degrees. Only focus on the clockwise rotation of OB around O by 105 ° to ob ? then ? aobc is a diamond
As shown in the figure, in the plane rectangular coordinate system, the coordinates of vertex B of diamond oabc are (8,0) and vertex A is on the image of function y = 12 / X (x > 0) Find the side length of diamond
I don't know why I can't see the graph, but since the problem is diamond, that is to say, the side length is equal, that is, OA = ab
Then point a must be on the vertical bisector of the line segment formed by point O and point B, that is, on the straight line x = 4. Then, the coordinates of the intersection point of the straight line and y = 12 / X (in fact, x = 4 is replaced) are (4,3). This is the coordinates of point a, and then OA = 5 is the side length
As shown in the figure, lozenge oabc is placed in the plane rectangular coordinate system, point a is on the positive half axis of X axis, point B is in the first quadrant, and its coordinates are (8,4). Parabola y = AX2 + BX + C passes through points o, a and C (2) The diamond is translated to the left, and the intersection point of parabola and segment AB is set as D to connect CD ① When point C is on the parabola again, find the coordinates of point D; ② When △ BCD is a right triangle, find the translation distance of diamond
In RT Δ ABB ', AB ^ 2 = AB ^ 2 = ab' ^ 2 + BB '^ 2,; ab ^ 2 = 64-16ab + AB ^ 2 + AB ^ 2 = 64-16ab + AB ^ 2 + 16, ab = 5, a (5,0), C (3,4), substitute into the quadratic function analytic formula: 0 = C0 = 25A + 5B + C4 = 9A + 3B + C, the solution: a = - 2 / 3, B = 10 / 3, C = 0, the solution is: a = - 2 / 3, B = 10 / 3, C = 0, C = 0, the solution is: a = - 2 / 3, B = 10 / 3, C = 0, the solution is: a = - 2 / 3, B = 10 / 3, C = 0, the solution is: a = - 2 / 3, B = 10 / 3, the formula is as follows
Let the left and right vertices of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 are A.B, O is the origin of coordinates, and the product of slope of straight line AP and BP is 1 / 2
Let P (XO, yo) KAP * kbp = [yo / (xo-a)] * [yo / (XO + a)] = - 1 / 2, the result is: XO ^ 2 + 2yo ^ 2 = a ^ 2
RELATED INFORMATIONS
- 1. In the rectangular coordinate system xoy, point B and point a (- 1,1) are symmetric about the origin o, P is a moving point, and the product of slope of straight line AP and BP is equal to - 1 / 3 Drawing and finding that APB and MPN are complementary sinAPB=sinMPN PA/PM=PN/PB.a (x0+1)/(3-x0)=(3-x0)/(x0-1).b Why can a write B
- 2. In the plane rectangular coordinate system x0y, the coordinates of the parallelogram A and B are (2,3), (5,1), respectively (1) If point C is on the positive half axis of the X axis and D is on the positive half axis of the Y axis, write the coordinates of the vertices C and D (2) If (1) condition is changed to point C and D on the coordinate axis, write the coordinates of C and D Ask God to answer, correctly add points
- 3. Given the point a (- 4,0) B (2,0), if the point is on the image of the linear function y = - 2 / 1X + 2 and the triangle ABC is a right triangle, several conditions of point C are satisfied
- 4. As shown in the figure, in the plane rectangular coordinate system xoy, the vertex e coordinates of rectangular oefg are (4,0), and the vertex g coordinates are (0,2). Rotate the rectangular oefg anticlockwise around point O, so that point F falls on the point n of the Y axis, and the rectangle omnp, OM and GF intersect at point a (1) Judge whether △ OGA and △ NPO are similar and explain the reasons; (2) The analytic formula of inverse proportional function of point a is obtained; (3) If the image of the inverse scaling function obtained in (2) intersects with EF at point B, please explore whether the line AB is perpendicular to OM and explain the reason
- 5. It is known that the radii R1 and R2 of the two circles are two of the equations x2-7x + 10 = 0, and the distance between the centers of the two circles is 7, then the position relationship between the two circles is______ .
- 6. Find the distance between the parallel lines 3x-2y-5 = 0 and 6x-4y + 3 = 0
- 7. If the equation of the circle is the square of X + the square of Y - 2x + 4y-20 = 0, find the linear equation of the diameter of the origin
- 8. Over the point（ 3, − 2) passes through the center of circle x2 + y2-2y = 0, then the inclination angle of line L is () A. 30° B. 60° C. 150° D. 120°
- 9. If there is no real root in the quadratic equation x ^ 2 + (M + 2) x + (1 / 4) m ^ 2 = 0, the root number m ^ 2 + │ M-1 │
- 10. It is known that the eccentricity of the ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is the root 5 / 3, and the distance from one end point of the minor axis to the right focus is 3
- 11. As shown in the figure, in the plane rectangular coordinate system, ⊙ P and X axis are tangent to origin o, and the straight line parallel to y axis intersects ⊙ P at M and N. if the coordinates of point m are (2, - 1), then the coordinates of point n are () A. （2，-4） B. （2，-4.5） C. （2，-5） D. （2，-5.5）
- 12. In the plane rectangular coordinate system, the coordinate of point a is (4,0), and the point P is on the straight line y = x-m, and AP = OP = 4
- 13. In the rectangular coordinate system, the first order function y = x + m and the inverse proportional function y = m / X intersect point a in the first quadrant, intersect point C with X axis, AB is perpendicular to X axis, perpendicular foot is B, and the area of triangle ABO is 1
- 14. The coordinates of the three vertices of △ ABC are a (1, - 1), B (4, 1) and C (2, 2). When △ ABC is rotated 180 ° around the origin of the coordinates, the coordinates of each vertex of the triangle are as follows______ ，______ ，______ .
- 15. The vertex coordinates of the triangle are a (2, 2), B (4, 2), C (6, 4). Try to reduce △ ABC so that the corresponding side ratio of △ def and △ ABC is 1:2
- 16. In the rectangular coordinate system, the circle with point a (root 3,0) as the center and radius 2 and 3 as the radius intersects the X axis at B, C. and Y axis at D, e.50-
- 17. It is known that the three points in the plane rectangular coordinate system are a (1, - 1), B (- 2,5) C (4, - 6) are used to judge whether the passing point a, B and C3 can be in a circle
- 18. Circle O1 the radius of circle O2 is R.R, the distance between centers of circle is D, and the two circles are outward. Point P moves on circle O1, and point Q moves on circle O2. The maximum of PQ is asked The radius of circle O1 and circle O2 are R.R, D and D respectively. Point P moves on circle O1 and point Q moves on circle O2. What are the maximum and minimum values of PQ and why? I already know the answer. = = if you want to score, please answer it carefully!
- 19. As shown in the figure, circle O1, circle O2, circle O3 are tangent to each other and O1O2 = 2, o1o3 = 4, O2O3 = 4, find the radius of circle O1, circle O2 and circle O3
- 20. Let the circle O1. The radius of circle O2 is R1 and R2 respectively. If circle O2 is on the circumference of circle O1, what is the distance between O2 and common chord?