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One step of the math problem in the college entrance examination is not to understand how it came from. . 20 13 national curriculum standard 1, please advise! Thank you!
Is it the yellow part? This is the chord length formula can be derived!

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? )