The coordinates of the intersection of the line y = 2x and the hyperbola y = 1 / X are_______ Speed! All the teachers and students come to watch The answer is attached with the detailed problem solving process

（-√2/2,√2）（√2/2,√2）
2X = 1 / x, 2x * x = 1, x = + - (√ 2 / 2),

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1. The coordinates of the intersection of the line y = 2x and the hyperbola y = 6 / X are
2. If there is an intersection (2,4) between the straight line y = 2x and the hyperbola y = 8 / x, then their other intersection is?
3. What is the intersection coordinate of parabola y = - 2x ^ 2-x + 3 and Y axis? What is the intersection coordinate of parabola y = - 2x ^ 2-x + 3 and X axis?
4. It is known that the parabola y = x ^ 2-2x-8 (2) If the two intersections of the parabola and the x-axis are ab respectively, and its vertex is p, the area of the triangle ABP is calculated
5. The tangent of parabola y = x2 at point P is perpendicular to the straight line 2x-6y + 5 = 0. The coordinate and tangent equation of point P are obtained Let's talk more about how the slope comes from
6. Why is the tangent equation parallel to the parabola y = x & # 178; with the straight line 2x-y + 4 assumed to be X & # 178; - 2x-c = 0
7. If the point P on the parabola y = x & # 178 is tangent L and the tangent L is perpendicular to the straight line 2x-y-5 = 0, then the equation of tangent L is,
8. If the distance from a point m on the parabola y = 4x2 to the focus is 1, then the ordinate of point m is () A. 1716B. 1516C. 78D. 0
9. If the tangent of point P passing through the parabola y = x ^ 2 is parallel to the straight line 4x-y-5 = 0, then the coordinate of point P is the tangent equation passing through point P?
10. Given that the angle between the tangent line at point P on parabola y = x ^ 2 and the straight line y = 3x + 1 is (PAI / 4), try to find the coordinates of point P Let P exit slope k | K-3 | / | 1 + 3K |
11. 1. The coordinate of the intersection of hyperbola y = 8 / X and straight line y = 2x is? 2. If the inverse scale function image passes through point a (1,2), then when x
12. The following propositions are given: proposition 1. The point (1,1) is an intersection of the straight line y = x and the hyperbola y = 1x; Proposition 2. The point (2,4) is an intersection of the straight line y = 2x and the hyperbola y = 8x; proposition 3. The point (3,9) is an intersection of the straight line y = 3x and the hyperbola y = 27x (1) please observe the above proposition and conjecture proposition n (n is a positive integer); (2) use the conjecture of the above question to directly write the solution of inequality 2010x > 20103x
13. The intersection coordinates of hyperbola y = 8x and straight line y = 2x are______ ．
14. Given that the Quasilinear of the parabola y2 = 2px coincides with the left quasilinear of the hyperbola x2-y2 = 2, the focal coordinate of the parabola is______ ．
15. If the left focus of hyperbola x23 − 16y2p2 = 1 is on the Quasilinear of parabola y2 = 2px, then the value of P is () A. 2B. 3C. 4D. 42
16. Given that the focus F of the parabola y2 = 2px (P > 0) is exactly the right focus of the hyperbola x2a2-y2b2 = 1 (a > 0, b > 0), and the hyperbola passes through the point (3a2p, B2P), then the asymptote equation of the hyperbola is () A. y=±2xB. y=±xC. y=±5xD. y=±153x
17. It is known that parabola y ^ 2 = 2px (P > 0) and hyperbola x ^ 2 (radical 2-1) ^ 2-y ^ 2 / b ^ 2 = 1 have the same focus F, point a is the focus of two curves, and AF is vertical On the x-axis, the line L and the parabola intersect at two different points c, D If the vector OC * od = m (M is a constant) and the line l only passes through a unique point, the value of M and this point can be obtained
18. As shown in the figure, in the plane rectangular coordinate system, the parabola y = - 1 / 2x & # 178; + 3 / 2x + 2 intersects X axis at two points a and B, and intersects Y axis at point C (1) ABC is a right triangle (2) : the straight line x = m (0 ∠ m ∠ 4) moves on the line ob, intersects the x-axis at point D, intersects the parabola at point E, intersects BC at point F. when m = what, EF = DF? (3) : after connecting CE and be, "is there a point e to maximize the area of triangle BCE?" if there is a point E, calculate the coordinates of point E and the maximum area of triangle BCE
19. Find the area of the figure surrounded by X & # 178; + Y & # 178; = 2, X & # 178; + Y & # 178; = 4x, y = x, y = 0
20. Find the area of the figure enclosed by the parabola y = x ^ 2 and y = 2x ^ 2, and find the volume of the solid figure formed by the figure rotating around the X axis