Given that the distance from a point P on the parabola y2 = 16x to the x-axis is 12, then the distance from P to the focus f is equal to 12______ ．

Given that the distance from a point P on the parabola y2 = 16x to the x-axis is 12, then the distance from P to the focus f is equal to 12______ ．

According to the meaning of the question, we can know that the ordinate of point P | y | = 12, and substitute it into the parabolic equation to get x = 9. The Quasilinear of the parabola is x = - 4. According to the definition of the parabola, we can know that the distance between point P and focus f is 9 + 4 = 13, so the answer is: 13

Given that point m is any point of the parabola y ^ 2 = 2px (P > 0), f is the focus of the parabola, if MF is taken as the diameter of the circle, then the position relationship between the circle and the y-axis

Tangency
As shown in the figure:
According to the definition of parabola, there is | MC | = | MF | = D (D is the diameter),
|DF|=p
∴|AB|=(|MC|+|DF|)/2=(d+p)/2
| AE | = | ab | - | be | = (D + P) / 2 - P / 2 = D / 2 = R (R is radius)
‖ tangent
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If (4, m) is a point on the parabola y = 2px, f is the focus of the parabola, and | PF | = 5, then
The equation is ()

P (4, m) is a point on the parabola y ^ 2 = 2px, P > 0
And: m ^ 2 = 2p * 4 = 8p
F is the focus of parabola, f (P / 2,0)
|PF|^2=(4-p/2)^2+(m-0)^2
=16-4p+p^2/4+m^2
=16+4p+p^2/4
=(4+p/2)^2
So, 4 + P / 2 = 5
p=2
The parabolic equation is y ^ 2 = 4x