The first problem can be solved by the undetermined coefficient method. The second question, if O is OM vertical BC, then OM= root number 2, because OB= root number 10, MB=2 root number 2 can be obtained according to Pythagorean theorem.
Solution: (1) Because the parabola y = ax 2+bx (a is not equal to 0) passes through B(3, 1) A, b, C(- 1, -3), the detailed answer is here/exercise/math/80056544. Where B(3, 1), C(- 1, -3), the straight line CO intersects the hyperbola at another point d, and the parabola intersects the x axis at another point e. 。
(1) Find the analytic expressions of hyperbola and parabola;
(2) Does the parabola have a little p in the first quadrant, so that ∠POE+∠BCD=90 degrees? If it exists, request the coordinates of the points that meet the conditions; If it does not exist, please explain the reason;
(3) As shown in Figure 2, the straight line L is perpendicular to OB, the intersection point D is DF where point F is perpendicular to L, and BD and OF intersect at point N to find the value of DN/NB.