1, let the standard equation of parabola be y? = 2px(p & gt； 0), the focus is F(p, 0). The equation of straight line AB can be set as y=k(x-p), where k is the slope. Substitute the equation of straight line AB into the equation of parabola to get: k? (x？ -2px+p？ ) =2px. Tidy up: K? x？ -(2p+2pk？ )x+k？ p？ =0。
2. According to Vieta's theorem, the intersection point A(x? ，y？ ) and B(x? ，y？ Is the sum of the abscissas x? +x？ =(2p+2pk？ )/k？ . Using the chord length formula, the chord length |AB|=|x? -x？ |√( 1+k？ )。 For a straight line CD, the equation passing through the focal point f can be set as y=-k(x-p). Similar to AB, we can get |CD|=|x? -x？ |√( 1+k？ )。
3. Combining the lengths of AB and CD, the total chord length is |AB|+|CD|=2p/k? *√( 1+k？ )。 This formula can be used to calculate the focal chord length for a given parabolic equation and focal chord length slope. It can also be used to solve geometric problems related to parabola.
The benefits of learning mathematics
1. Mathematics is a highly logical subject, and learning mathematics can help you exercise your logical thinking ability. This ability allows you to better analyze problems, reason and judge, so as to better solve various problems in life. Math problems usually need to be solved by what you have learned, and learning math can help you improve your problem-solving ability.
2. This ability can make you better adapt to all kinds of complicated situations and better cope with the challenges in life. Learning mathematics requires patience and perseverance, because it often takes a lot of time and energy to solve mathematical problems. By studying mathematics, you can cultivate your patience and perseverance, so as to better cope with all kinds of difficulties in life.
When you solve a math problem through your own efforts, you will feel a sense of accomplishment. This sense of accomplishment can enhance your self-confidence and make you more confident to cope with various challenges. Studying mathematics can help you better understand other subjects, such as physics, chemistry and economics.