"That's right, what's so great about being able to do the question just now? At least half of the students in our class can do it too!"

While the students in the audience were talking quietly, Zheng Jianzhou's topic had been written.

"The right vertex of ellipse E: x^2/a^2+y^2/b^2=1 (a is greater than b is greater than 0) is A, the right focus is F, and the upper and lower vertices are B, C, |AB|

=7 ^(1/2), straight line CF intersects line segment AB at point D, and |BD|=2|DA|,

(1) Find the standard equation of E;

(2) Is there a straight line l such that l intersects the ellipse at two points M and N, and F is exactly the vertical center of △BMN? If it exists, find the equation of l; if it does not exist, explain the reason."

If the question about the sum of geometric series just now was just an ordinary question with over-the-top knowledge points, then this question was what Zheng Jianzhou planned to use as the finale of the next monthly exam.

Lao Zheng was extremely confident about the difficulty of this question, which required strong spatial thinking and problem-solving abilities. He expected that even Wu Shaocai, the math subject representative in the class, might not be able to solve it in five minutes...

"Qin Ke, you come to solve this problem. I will also give you three minutes. You can use a pen..." Zheng Jianzhou turned his head and was only halfway through his words when Qin Ke interrupted: "First question, ellipse E

The standard equation of is x^2/4+y^2/3=1. The second question is, there is a straight line l such that F is the orthocenter of △BMN, and the equation of l is y=3^(1/2)x/3-16

*3 ^(1/2)/21.”

Zheng Jianzhou subconsciously looked through the answers and found that they were all correct.
Chapter completed!