To say "chord length formula" is actually the distance formula between two points-because the slope k is known, it can be expressed by slope and abscissa (or ordinate).

Because this formula is often used to find the distance between two points on a conic curve, it is usually called "chord length formula"

Derived as follows:

From the slope formula of the straight line: k = (y 1-y2)/(x 1-x2)

Get y 1-y2 = k(x 1-x2) or x1-x2 = (y1-y2)/k-y2)/k.

Substitute the distance formula between two points: |AB| = √[(x 1-x2)? + (y 1 - y2)？ ]

After a little sorting, it is concluded that:

|AB| = |x 1 - x2|√( 1 + k？ ) or | ab | = | y1-y2 | √ (1+1/k? )