The minimum distance between the point on the parabola y ^ = 8x and its focus is equal to?

The minimum distance between the point on the parabola y ^ = 8x and its focus is equal to?

Since the distance from the point on the parabola y ^ 2 = 8x to its focus (2,0) is the same as that to the collimator x = - 2, the distance from the point on the parabola y ^ 2 = 8x to its focus is the same
d=|x+2|>=2(x>=0)
The minimum value is 2

On the parabola y ^ 2 = 8x, the distance from a point m to the focus is 5, and the abscissa of the distance m from the point m to the collimator
On the parabola y ^ 2 = 8x, the distance from a point m to the focus is 5, and the abscissa of the distance m from the point m to the collimator

Definition of parabola
The distance from m to the focus is equal to the distance to the guide line
So the distance from m to the guide line is 5
2p=8
p/2=2
So the guide line x = - 2
M distance to guide line = 5
So m abscissa = 5-2 = 3

If the distance between a point P and its focus on the parabola y ^ 2 = 8x is 9, then the coordinate of point P is?

Solution
Parabola y & #178; = 8x
Quasilinear equation: x = - 2
The abscissa of point P is 7
∴y=±2√14
∴P(7,±2√14)

Let the distance from a point P on the parabola y ^ 2 = 8x to the Y axis be 4, then the distance from the point P to the focus of the parabola?

The parabolic quasilinear equation x = - P / 2, the focus is (P / 2,0),
According to the parabola y ^ 2 = 8x, the focus is (2,0), x = - 2
Therefore, according to the definition of parabola, the distance from point P to focus is 2 + 4 = 6

If the distance between the point P on the parabola y square = 8x and its focus f is 10, what is the distance between the point P and the straight line x = 4,

If the Quasilinear equation of Y square = 8x is x = - 2, then the distance from P to the Quasilinear is 10. If the abscissa of P is x, then x - (- 2) = 10, x = 8
The distance from P to the straight line x = 4 is: x-4 = 8-4 = 4

Given the point a (3,4), f is the focal point of the parabola y2 = 8x, M is the moving point on the parabola, when | Ma | + | MF | is the minimum, the coordinates of point m are ()
A. （0，0）B. （3，26）C. （2，4）D. （3，-26）

Let the directrix of the parabola be l, MB ⊥ l over M to B, AC ⊥ l over a to C. from the definition of the parabola, we know that | MF | = | MB | {| Ma | + | MF | = | Ma | + | MB | ≥ | AC | (the broken line is larger than the vertical line), if and only if a, m and C are collinear, take the equal sign, that is | Ma | + | MF | minimum. At this time, the ordinate of M is 4, and the abscissa is 2, so m (2, 4) is selected as C

Sine theorem (30 21:16:56)
In the triangle ABC, the opposite sides of angles a, B and C are a, B and C respectively, Tana = 1 / 2, CoSb = (3 √ 10) / 10. If the length of the longest side of triangle ABC is 1, the length of the shortest side is & # 160; &# 160; &# 160; &# 160; &# 160; &# 160; &# 160; &# 160; &# 160; &# 160; if the length of the longest side of triangle ABC is 1;

Tana = Sina / cosa = 1 / 2, Sina = √ 5 / 5, CoSb = (3 √ 10) / 10, SINB = √ 10 / 10, Sina > SINB, so a > b if a is the longest, B = √ 2 / 2, C = √ 10 / 2 > 1, C is the longest, C = 1, and B is the shortest, COSC = - √ 2 / 2, sinc = √ 2 / 2, so B = √ 5 / 5, so the length of the shortest side is √ 5 / 5

Please answer the math set of senior one in detail, thank you! (8 21:56:1)
There is such a problem in the explanation of set examples: let a = {x | - 2 ≤ x ≤ a}, B = {y = 2x + 3, X ∈ a}, C = {z = x ^ 2, X ∈ a}, and B &; C. find the value range of real number a
Analysis: to satisfy the inclusion relation between B and C, we must know the elements of set B and C
The value range of Y in B is # - 2 ≤ x ≤ a, y = 2x + 3, so - 1 ≤ y ≤ 2A + 3
How to calculate: - 1 ≤ y ≤ 2A + 3

x∈A
That is - 2 ≤ x ≤ a
So - 4 ≤ 2x ≤ 2A
So - 4 + 3 ≤ 2x + 3 ≤ 2A + 3
That is - 1 ≤ y ≤ 2A + 3

Function (7 19:58:52)
When the surface air temperature is 20 ℃, and the air temperature drops by 6 ℃ for every 100 m rise, the analytic expression of the function between the air temperature T (  ℃) and the height h (m) is (                                &#

Let the temperature T (℃) be a linear function of height h (m), and its analytical formula is t = KH + B,
When h = 0, t = 20; when h = 100, t = 20-6 = 14
20=b
14=100k+b
The solution is: k = - 0.06, B = 20. The analytical formula is: T = - 0.06h + 20

Circle (19 18:58:53)
The secant of circle: x2 + y2 = 9 is called circle O at a and B. find the trajectory equation of point P in ab

Let P point coordinate (x, y). AB coordinate be (x1, Y1), (X2, Y2) respectively. According to the problem, we can get the following five formulas: X1 ^ 2 + Y1 ^ 2 = 9 (1) X1 ^ 2 + Y1 ^ 2 = 9 (2) (because AB is on the circle) (y1-y2) / (x1-x2) = (y + 4) / (X-2) (3) (abpq four points collinear) X1 + x2 = 2x (4) Y1 + y2 = 2Y (5) (P is in ab