It is known that the line and parabola y2 = 2px (P > 0) intersect at two points a and B, and OA ⊥ ob, OD ⊥ AB intersect at D, and the coordinate of point D is (2,1), then the value of P is () A. 52B. 23C. 54D. 32

Let a (x1, Y1), B (X2, Y2), ∵ line od slope be 12, OD ⊥ AB, and ≁ line AB slope be - 2, so the linear AB equation is 2x + Y-5 = 0 (1) Substituting (1) into parabolic equation, we get Y2 + py-5p = 0, then y1y2 = - 5p, ∵ Y12 = 2px1, Y22 = 2px2, then (y1y2) 2 = 4p2x1x2, so x1x2 = 25

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1. Points a and B are two moving points beyond the origin of the parabola y ^ 2 = 2px (P > 0), and OA is perpendicular to ob, Let a (x1, Y1), B (X2, Y2) find the values of Y1 * Y2 and X1 * x2
2. Let a (x1, Y1), B (X2, Y2) be two points on the parabola y2 = 2px (P > 0) and satisfy OA ⊥ ob. Then y1y2 is equal to () A. -4p2B. 4p2C. -2p2D. 2p2
3. If the line AB passes through the fixed point (2P, 0), it is proved that OA is perpendicular to ob,
4. A. B is two points on the parabola y ^ 2 = 2px, and OA is perpendicular to ob (o is the origin of coordinates). This paper proves that the product of abscissa and ordinate of a and B are fixed values
5. The parabola passes through the origin o, the point a (6,8), and the point (3, - 5). If the line BC parallel to the Y-axis of point B on the line OA intersects with the parabola at C, △ OBC isosceles Find the coordinates of point C
6. If the line L passing through the point (0, - 1 / 2) intersects with the parabola: y = - x * x at two points a and B, and O is the origin of the coordinate, then the value of the vector of OA multiplied by OB is?
7. As shown in the figure, the parabola is symmetric about X axis, its vertex is at the origin of coordinates, and the points P (1,2), a (x1, Y1), B (X2, Y2) are all on the parabola. (I) write out the equation of the parabola and its quasilinear equation; (II) when the slopes of PA and Pb exist and complement each other, find the value of Y1 + Y2 and the slope of line ab
8. The known parabola y = - x square + 2 (k-1) x + K + 2 10 - 14 days and 23 hours to the end of the problem It intersects with X axis at two points AB, and point a is on the negative half axis of X, and point B is on the positive half axis of X Question: (1): find the value range of real number K (2) Let the lengths of OA and ob be a and B respectively, and a: B = 1:5 ,
9. It is known that the square of parabola y = negative X and the line y = K (x + 1) intersect at two points a and B
10. It is known that the parabola y squared = - x intersects the straight line L: y = K (x + 1) at two points a and B (1) OA vertical ob (2) When the area of the triangle OAB is equal to the root 10, the value of K is obtained
11. As shown in the figure, it is known that a straight line and a parabola y ^ 2 = 2px intersect with two points a and B, and OA is perpendicular to ob, OD is perpendicular to AB, and ab intersects with point D. the coordinates of point D are (2,1), and the value of P is obtained
12. It is known that the straight line and parabola y & # 178; = 2px (P > 0) intersect at two points a and B, and OA ⊥ ob, OD ⊥ AB intersect at point D, and the coordinates of point D are (2,1), Let's find the value of P instead of a vector,
13. Given that the straight line and parabola y ＾ 2 = 2px intersect at two points AB, and OA ⊥ ob, OD ⊥ AB intersect at D, D coordinate is (2,1), find the value of P First, I calculate the slope k of OD with the coordinates of point D, and then calculate the slope k 'of ab. because AB passes through D, we can know the equation of ab Then, the equation AB is substituted into the parabola, and the x 1 + x 2 and X 1x 2 are calculated by the Weida theorem Then, let a (x1, root 2px1), B (X2, root 2px2), calculate the algebraic formula of OA, OB length, because OA ⊥ ob, so the area is oaob / 2 Then calculate the length of AB section parabola, OD length and area abod / 2 with chord length formula Finally, because the two areas are equal, abod / 2 = oaob / 2, and then combined with vedadine to understand P
14. A. B is two points on the parabola y ^ 2 = 2px (P > 0), which satisfies OA vertical ob (o is the origin), and proves that the straight line AB always passes a certain point How did you get the answer at the last step? I don't understand Or is there a better solution How to find (Y1 + Y2) * y = 2p (x-2p)?
15. Let a straight line L with a slope of 1 pass through the focus of the parabola y ^ 2 = 4x and intersect with the parabola at two points a (x1, Y1); B (X2, Y2), then the vector OA × the vector ob=
16. In RT △ ABC, what is the position relationship between the circle with C as the center and R as the radius and ab? （1）r=2cm （2）r=2.5cm （3）r=3cm
17. In RT △ ABC, ∠ C = 90 °, AC = 3cm, BC = 4cm, with C as the center, what is the positional relationship between the following r-radius circle and ab? r=2.4cm And R = 3cm
18. As shown in the figure, there is a right triangle paper with two right sides AC = 6cm and BC = 8cm. Now fold the right side AC along the straight line ad so that it falls on the hypotenuse AB and coincides with AE, then CD is equal to () A. 2cmB. 3cmC. 4cmD. 5cm
19. As shown in the figure, in △ ABC, ab = 8cm, BC = 16cm, point P starts from point a, moves along edge AB to point B at a speed of 2cm / s, and point Q starts from point B, moves along edge BC to point C at a speed of 4cm / s. if points P and Q start from point a and B at the same time, after a few seconds, △ PBQ is similar to △ ABC? Try to explain the reason
20. In RT triangle ABC, angle B = 90 ', ab = 6 cm, BC = 8 cm. Point P starts from a and follows ab If points P and Q start from points a and B at the same time, then after a few seconds, the distance between two points P and Q is 53 cm? I use words to describe the symbols. Please read the meaning of the words clearly. Write the equation of one variable and degree