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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
If point F (1,1) is on the straight line 3x + y-4 = 0, then the trajectory of point P is a straight line passing through point F (1,1) and perpendicular to the known straight line. Because the slope of the straight line 3x + y-4 = 0 is - 3, the slope of the straight line is 13. From the oblique form of the point, we know that the trajectory equation of point P is Y-1 = 13 (x-1), that is, x-3y + 2 = 0, so we choose B
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______ ．
The distance from point P to point F (4,0) is 1 less than the distance from point P to line x + 5 = 0, and the distance from point P to line x = - 4 is equal to the distance from point P to point (4,0). According to the definition of parabola, the trajectory of point P is a parabola with point (4,0) as the focus and line x = - 4 as the guide line, and the trajectory equation of point P is y2 = 16x
RELATED INFORMATIONS
- 1. 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______ ．
- 2. 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
- 3. How many days are there from August 20, 2009 to February 12, 2014?
- 4. How many days have passed since April 5, 2014 to July 28, 2011
- 5. How many days are there from December 18, 2012 to June 8, 2014? How many hours are there?
- 6. How many days are there from May 1 to October 31, 2010
- 7. How many days are there from May 1st to October 31st, 2010
- 8. How many days are there from February 1, 2012 to June 30, 2019?
- 9. How long does it take from March 8, 2013 to September 9, 2014
- 10. How many days are there from March 1, 2014 to February 28, 2015
- 11. 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)
- 12. 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
- 13. 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?
- 14. Find the trajectory equation of the point whose distance from the Y axis is equal to 4
- 15. The trajectory equation of a point whose distance from the X axis is equal to 2 is
- 16. 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
- 17. 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)
- 18. 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
- 19. If the distance between point m and point F (4,0) is less than 1, then the trajectory equation of point m is______ ．
- 20. 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