How to deduce the elliptic chord length formula? I can't deduce it How to deduce the formula of ellipse chord length Y = KX + B is brought into the elliptic standard equation. X ^ 2 / A ^ 2 + (KX + b) ^ 2 / b ^ 2 = 1, then

How to deduce the elliptic chord length formula? I can't deduce it How to deduce the formula of ellipse chord length Y = KX + B is brought into the elliptic standard equation. X ^ 2 / A ^ 2 + (KX + b) ^ 2 / b ^ 2 = 1, then

Chord length = │ x1-x2 │ √ (k ^ 2 + 1) = │ y1-y2 │ √ [(1 / K ^ 2) + 1]
Where k is the slope of the line, (x1, Y1), (X2, Y2) are the two intersections of the line and the curve
prove:
Suppose that the line is y = KX + B
Substituting into the equation of ellipse, we can get: x ^ 2 / A ^ 2 + (KX + b) ^ 2 / b ^ 2 = 1,
Let two intersections be a and B, point a be (x1.y1), point B be (x2.y2)
Then AB = √ (x1-x2) ^ 2 + (y1-y2)^
Substituting Y1 = kx1 + B and y2 = kx2 + B respectively,
The results are as follows:
AB=√（x1-x2)^2+(kx1-kx2)^2
=√(x1-x2)^2+k^2(x1-x2)^2
=√(1+k^2)*│x1-x2│
Similarly, it can be proved that: chord length = │ y1-y2 │ √ [(1 / K ^ 2) + 1]