The center is the origin, and the two focal points have a point P (3, t) on the ellipse on the x-axis. If the distance between the point P and the two focal points is 6.5 and 3.5 respectively, the elliptic equation is solved

The center is the origin, and the two focal points have a point P (3, t) on the ellipse on the x-axis. If the distance between the point P and the two focal points is 6.5 and 3.5 respectively, the elliptic equation is solved

Let the two focal points of the ellipse be F1 and F2
So Pf1 + PF2 = 6.5 + 3.5 = 10 = 2A, so a = 5
Let F1 coordinate (- C, 0) F2 coordinate (C, 0)
So according to the distance formula: (3 + C) ^ 2 + T ^ 2 = 42.25. (1)
(3-c)^2+t^2=12.25.(2)
(1) - (2) formula (3 + C) ^ 2 - (3-C) ^ 2 = 30, solution c = 2.5
Because B ^ 2 = a ^ 2-C ^ 2, the solution is B ^ 2 = 75 / 4
So the elliptic equation is: x ^ 2 / 25 + (4 * y ^ 2) / 75 = 1

If the center of a moving circle is on the parabola y2 = 8x and the moving circle is always tangent to the straight line x + 2 = 0, then the moving circle must pass the fixed point ()
A. （0，2）B. （0，-2）C. （2，0）D. （4，0）

∵ the Quasilinear equation of the parabola y2 = 8x is x = - 2, ∵ from the problem, we can see that the center of the moving circle is on y2 = 8x, and it is always tangent to the Quasilinear of the parabola. From the definition, we can see that the moving circle always passes the focus of the parabola (2,0), so we choose C

If the center of a moving circle is on the parabola y2 = 8x and the moving circle is always tangent to the straight line x + 2 = 0, then the moving circle must pass the fixed point ()
A. （0，2）B. （0，-2）C. （2，0）D. （4，0）

∵ the Quasilinear equation of the parabola y2 = 8x is x = - 2, ∵ from the problem, we can see that the center of the moving circle is on y2 = 8x, and it is always tangent to the Quasilinear of the parabola. From the definition, we can see that the moving circle always passes the focus of the parabola (2,0), so we choose C

If the center of the moving circle is on the parabola y ^ 2 = 8x, and the moving circle is always tangent to the straight line x = - 2, then the moving circle must pass through the fixed point, and its fixed point coordinate is

The focal coordinate of parabola y ^ 2 = 8x is (2,0) and the Quasilinear equation is x = - 2
According to the definition of parabola, the distance from a point on the parabola to the focus is equal to the distance from the point to the directrix
It can be seen that the moving circle must pass the fixed point, and its fixed point is the focus, and the coordinate is (2,0)