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In the rectangular coordinate system, O is the origin of the coordinate, a (4,3). Find a point B on the coordinate axis, let △ OAB be an isosceles triangle List them one by one
Take 0 as the center and 5 as the radius to draw the arc. The intersection axis is composed of 4 points
Take a as the center of the circle, 5 as the radius, draw an arc, intersect coordinate axis 2 points (o point is not included)
Make a vertical line in Ao, intersect at 2 o'clock
Calculate the coordinates by yourself
If ⊙ P with P (3,4) as the center of the circle and the coordinate axis have four intersections, the range of its radius R is:______ ．
The distance between P (3,4) and X axis is 4, the distance between P (3,4) and Y axis is 3, the distance between P (3,4) and origin is 5, ⊙ P has four intersections with coordinate axis, ∵ r > 4 and R ≠ 5
RELATED INFORMATIONS
- 1. Take the point (1,0) as the center and 3 as the radius to draw a circle, then the coordinates of the intersection of the circle and the X axis are______ The coordinates of the point of intersection with the y-axis are_________
- 2. As shown in the figure, point B is on line ad, C is the midpoint of line BD, ad = 10, BC = 3. Find the length of line CD and ab
- 3. It is known that there are two points a and B in the two planes of dihedral angle α - L - β, and their projections in L are C, D, respectively It is known that there are two points a, B, a and B in the two planes of dihedral angle α - L - β. The projections of a, B, a and B in L are C, D, AC = 3, BD = 3, CD = 4 and ab = 5 respectively. The size of dihedral angle α - L - β can be obtained Why ∠ AEB = 90 °?
- 4. In mathematical geometry, there are two points a and B on the edge of a dihedral angle of 120 degrees. AC and BD are the dihedral angles respectively There are two points a and B on the edge of the dihedral angle of 120 degrees. AC and BD are the line segments perpendicular to AB in the two planes of the dihedral angle. Given AB = 4, AC = 6 and BD = 8, we can find the length of CD
- 5. If there is a line segment A.B on the plane with a length of 5, how many lines are there on the plane with distances of 2 and 3 from point AB?
- 6. If the distance between the two ends of line AB and plane α is equal to 1, then the position relationship between line AB and plane α is?
- 7. In the plane rectangular coordinate system, as shown in Figure 1, translate the line AB to the line CD, and connect AC and BD. (1) directly write out the equal line segments and parallel lines in the figure
- 8. It is known that the distance between a and B is 5cm. Find a point C in the plane so that the sum of the distances between point C and a and B is 5cm, then point C is in the plane? 1-4.2 exercises
- 9. If line AB is on the same side of plane α and the distances from a and B to α are 3 and 5 respectively, then the distance from the midpoint of AB to α is 0______ ．
- 10. Given that points a and B are on the same side of plane α and the distances to plane α are D and 3D respectively, then the distance from the midpoint of a and B to plane α is______ ．
- 11. In the plane rectangular coordinate system, the point whose abscissa and ordinate are integers is called integral point. Let the unit length of the coordinate axis be 1 cm, the integral point P starts from the origin o, and the velocity is 1 cm And point P can only move up or right When point P starts from point O for several seconds, the integral point (10,5) can be obtained
- 12. Does the origin belong to the axis?
- 13. In the plane rectangular coordinate system, if a (2,4), B (2, - 2), C (6, - 2) are known, then the coordinates of the center of the circle passing through a, B, C are______ ．
- 14. In the plane rectangular coordinate system, the known points a (- 3,0), B (0, - 4), C (0,1) pass through point C and make the intersection axis of the line at point D, so that points D, C, O In the plane rectangular coordinate system, known points a (- 3,0), B (0, - 4), C (0,1) pass through point C and make the intersection axis of the line at point D, so that the triangle with points D, C, O as the vertex is similar to △ AOB, such a line can make () A. One B. two C. four D. eight
- 15. Four points a (0,1) B (2,1) C (3,4) d (- 1,2) in the plane rectangular coordinate system. Can these four points be on the same circle? Why?
- 16. In Cartesian coordinate system, if the ordinates and abscissa of a point are all integers, then the point is called the integral point. Let K be an integer. When the intersection of the line y = x + 2 and y = KX + 4 is the integral point, how many values of K can be taken at most?
- 17. A point whose abscissa and ordinate are all integers is called an integral point. Let K be an integer. When the intersection of the line y = x-3 and y = KX + k is an integral point, how many points does K have From x-3 = KX = k to k = (x-3) / (x + 1), in order to further narrow the scope, how to simplify?
- 18. Draw a straight line y = - 2 / 3x + 7 / 3 in the rectangular coordinate system. If the line y = x-k intersects with it in the fourth quadrant, find the value range of K
- 19. The graph composed of all points with the solution of equation 3x + y = 5 as coordinates is a straight line () A.y=3x+5 B.y=3x-5 C.y=-3x+5 D.-3x-5
- 20. In the rectangular coordinate system, the origin of the coordinate is O, a (- 2,4), B (4,2) are known. (1) find the area of △ AOB; (2) find the point P on the x-axis to minimize the value of PA + Pb, and find the coordinate of point P