How to prove the curve equation of conic? Do you use definition?

How to prove the curve equation of conic? Do you use definition?

All your questions can be answered in elective 2 of high school mathematics textbook. I can tell you that the equations of conic curve are all obtained by analytical method, which means that the graph is placed in the plane rectangular coordinate system and the equations are obtained by algebraic method

On the problem of conic equation
1. If the chord of ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is made through point B (0, - b), find the maximum of these chord lengths
2. It is known that a, B and D are not on a straight line, and a (- 2,0), B (2,0), vector ad = 2, vector AE = 1 / 2 * (vector AB + vector AD)
(1) Find the trajectory equation of point E;
I've got x ^ 2 + y ^ 2 = 1 (y is not equal to 0)
(2) The distance between the middle point of Mn and Y-axis of the ellipse with a and B as the focus is 4 / 5, and the locus of Mn and e-point is tangent

Conic equation
It is known that the center of the ellipse is at the origin, and the directrix is x = plus or minus 4 times the root sign 2. If the projection of the intersection of the straight line x-root sign 2Y = 0 and the ellipse on the x-axis is exactly the focus of the ellipse, the equation of the ellipse is solved

Let the equation of the ellipse be X & sup2 / A & sup2; + Y & sup2 / B & sup2; = 1, the Quasilinear x = A & sup2; = 4 √ 2C A & sup2; > C & sup2; 4 √ 2C ＞ C & sup2; C (C-4 √ 2) ＜ 0, then 0 ＜ C ＜ 4 √ 2 B & sup2; = A & sup2; - C & sup2; = 4 √ 2c-c & sup2; the equation of the ellipse is X & S