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The distance between two fixed points is 6, and the sum of the squares of the distances from point m to these two fixed points is 26. Find the trajectory equation of point M
The midpoint of the line segment formed by these two points is the center, and the coordinate system is established
The coordinates of the two points are (- 3,0), (3,0) respectively. If the coordinates of the point m are (x, y), then according to the meaning of the title
[x-(-3)]^2+(y-0)^2+(x-3)^2+(y-0)^2=26
Simplify, simplify
x^2+y^2=4.
Given that the distance ratio between point m and two fixed points o (0,0), a (3,0) is 1 / 2, find the trajectory equation of point M
Given that the distance ratio of point m to two fixed points o (0,0), a (3,0) is 1 / 2, we can find the trajectory equation of point m. This is the problem we encountered when we studied the equation of circle
Let m (x, y)
Then am = 2om
So am ^ 2 = 4om ^ 2
That is, (x-3) ^ 2 + y ^ 2 = 4 (x ^ 2 + y ^ 2)
The trajectory equation of point m is (x + 1) ^ 2 + y ^ 2 = 4
Given that the distance between point m and X axis and the distance between point m and point F (0,4) are equal, the trajectory equation of point m is obtained
If M (x, y) is set as a moving point, then the distance between M and X axis and the distance between M and f (0, 4) are equal, that is, the trajectory equation of M is y = 18x2 + 2
Given that the distance from point m to point F (3,0) is 3 greater than the distance from point m to y-axis, the trajectory equation of point m is obtained,
It is known that the distance from point m to point F (3,0) is 3 times greater than the distance from point m to y-axis
Then the distance from point m to point F (3,0) is equal to the distance from it to the line x = - 3
So the trajectory of point m is a parabola
Let Y & # 178; = 2px
Then p / 2 = 3
So p = 6
So y & # 178; = 12x
RELATED INFORMATIONS
- 1. Teacher worldbl: the distance from the moving point m (x, y) to the y-axis is less than the distance from it to the fixed point (2,0). Find the trajectory equation of the moving point m (x, y)
- 2. If the distance from the moving point P to the x-axis is 2 less than the distance to the fixed point F (0,2), then the trajectory equation of the moving point is obtained
- 3. The trajectory equation of a point whose distance from the X axis is equal to 2 is
- 4. Find the trajectory equation of the point whose distance from the Y axis is equal to 4
- 5. If the distance from a moving point to point (2,0) is equal to half of the distance from it to point (8,0), then the trajectory equation of a moving point is?
- 6. If the distance from the moving point m (x.y) to the fixed point (1,1) is equal to the distance from m to the fixed line X-Y plus 1 equals 0, then the trajectory equation of the moving point m is? If the distance from the moving point m (x.y) to the fixed point (1,1) is equal to the distance from m to the fixed line X-Y plus 1 equals 0, then the trajectory equation of the moving point m is
- 7. The distance between a moving point and a straight line x = 8 is twice as long as the distance between it and point a (2.0)
- 8. If the distance from the moving point P to the point F (1,1) and the straight line 3x + y-4 = 0 is equal, then the trajectory equation of point P is () A. 3x+y-6=0B. x-3y+2=0C. x+3y-2=0D. 3x-y+2=0
- 9. If the distance from point P to point F (4,0) is less than the distance from point P to line x + 5 = 0 by 1, then the trajectory equation of moving point P is______ ．
- 10. First simplify and then evaluate (- x ^ 3 + x ^ 2y-y ^ 3) - (x ^ 2-2xy ^ 2 + y ^ 3) + (2x ^ 2-3x ^ 2y-2xy ^ 2), x = 2009, y = - 1 / 2, Xiao Dong mistakenly copied x = 2009 to x = 2090, but the result he got was also correct. What do you mean
- 11. If the distance between point m and point F (4,0) is less than 1, then the trajectory equation of point m is______ ．
- 12. Given the point Q (2,0) and the circle C: x2 + y2 = 1 on the rectangular coordinate plane, when the ratio of the tangent length from the moving point m to the circle and MQ is 1 or 2 respectively, the trajectory equation of the point m is obtained
- 13. Given the point Q (2,0) and the circle O: X & # 178; + Y & # 178; = 1, the ratio of the tangent length from the moving point m to the circle to | MQ | is root 2, the trajectory equation of the moving point m is obtained For detailed explanation, please refer to the attached figure,
- 14. It is proved that the line connecting the two tangent points must pass through a certain point Such as the title
- 15. It is known that there are two points a (1,3), B (3,0) in the ellipse X225 + y216 = 1, and P is a point on the ellipse, then the maximum value of | PA | + | Pb | is______ ．
- 16. The eccentricity of ellipse e: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is e, P is the point on e, from P to the circle x ^ 2 + y ^ 2 = B ^ 2, make tangent PA and Pb, a and B are tangent points, Ask if there is a point P, so that PA ⊥ Pb? If there is, calculate the point P coordinate; if not, explain the reason
- 17. The projection of a point on the coordinate axis of the space coordinate system How to find. Can give an example to illustrate, as long as I can understand. Success can be + points How to find it when drawing
- 18. In Cartesian coordinates, the distance from the point P (- 1, (√ 3) / 2) to the origin o is
- 19. In Cartesian coordinates, the distance OP from point P (- 2,3) to the origin=______ ．
- 20. In the space rectangular coordinate system, the point a (1,0,2) B (1, - 3, - 1) m is on the Y axis, and the distance to a and B is equal In the space rectangular coordinate system, if the point a (1,0,2) B (1, - 3, - 1) m is on the Y axis and the distances to a and B are equal, then the coordinate of M is?