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______ ．

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

Given that the sum of the distances from the moving point m to the fixed points a (negative 9 / 4,0) and B (9 / 4,0) is 25 / 2, the trajectory equation of the point m is obtained

Obviously, the trajectory of the m-point is an ellipse
So C = 9 / 4, 2A = 25 / 2
a=25/4
b²=a²-c²=625/16-81/16=34
So the trajectory: X & sup2; / (625 / 16) + Y & sup2 / / 34 = 1
That is 16x & sup2 / 625 + Y & sup2 / 34 = 1

Given that the distance from the moving point m (x, y) to the fixed point (2, 0) is 1 less than the distance to the straight line x = - 3, then the trajectory equation of the moving point m is______ ．

∵ the distance from the moving point m (x, y) to the fixed point (2, 0) is 1 less than the distance to the straight line x = - 3, ∵ the distance from the moving point m (x, y) to the fixed point (2, 0) is equal to the distance to the straight line x = - 2. According to the definition of parabola, the trajectory of the moving point m is a parabola, and its equation is y2 = 8x

Simplify first, then evaluate: 2x ^ 2 √ (1 / x) - 3 √ (x ^ 3) + √ (4x ^ 3), where x = 1.69

The original formula for the original formula = 2x and35\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\.3 = 2.197