Given that the line y = x + 1 and parabola y2 = ax intersect at two points a and B, if OA vector multiplies ob vector = A2-1, find the value of real number a

a=2or-1

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1. If there are three different points on the line L, so that the equation x ^ 2 vector OA + X vector ob + vector BC = vector 0 has a solution, (o is not on L), find the real number solution set x^2*OA+x*OB+BC=0 BC=-(x^2*OA+x*OB) BC=OC-OB OC-OB=-(x^2*OA+x*OB) OC= - x^2*OA - x*OB + OB Because three points are collinear - x^2 - x* +1=1 - x^2 - x*=0 x(x+1)=0 X = 0 or 1 Because when x = 0, the three points coincide, which is not in line with the meaning of the topic So x = - 1 Why? OC= - x^2*OA - x*OB + OB Because three points are collinear So - x ^ 2 - x * + 1 = 1
2. It is known that the two focuses of the hyperbola are F1, F2, one of the imaginary axes, the endpoint B, and the angle f1bf2 = 2 π / 3, so the eccentricity of the hyperbola can be obtained
3. The left and right focus of the hyperbola x ^ 2 △ a ^ 2-y ^ 2 △ B ^ 2 = 1 is F1 and F2. The point P is on the hyperbola, and Pf1 = 4 is known. The maximum value of the eccentricity of the hyperbola is obtained The options are a.4 / 3 B.3 / 2 C.5 / 3 D.2
4. Given that the left and right focus of hyperbola are F1 and F2 respectively, P is a point on hyperbola, and Pf1 ⊥ PF2, pf1pf2 = 4AB, then the eccentricity of hyperbola is ■
5. Hyperbola: two focuses of x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0) are F1, F2, P are a point on the hyperbola, and Pf1 = 3PF2, then the value range of eccentricity
6. The two focuses of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0) are F1 and F2. If P is the upper point and | Pf1 | = 2 | PF2 |, the value range of hyperbolic eccentricity is () A. （1，3）B. （1，3]C. （3，+∞）D. [3，+∞]
7. If | PF2 | ^ 2 / | Pf1 | = 8a, what is the range of eccentricity
8. P is the point on the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), F1 and F2 are its focus, the eccentricity of the hyperbola is 5 / 4, and the vector pf * vector PF2 = 0, If the area of triangle f1pf2 is 9, find the value of a + B
9. It is known that F 1 and F 2 are the focus of hyperbola x ^ / A ^ - y ^ / b ^ = 1 (a > 0, b > 0), P is on the right branch, and Pf1 = 4pf 2. The range of eccentricity of hyperbola is obtained
10. The two focuses of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 are F1 and F2. If P is the upper point and lpf1l = 2lpf2l, the value range of hyperbolic eccentricity is
11. Given that the left and right focal points of hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1 are F1 and F2 respectively, P is a point on the right branch of hyperbola, and | PF2 | = | F1F2 |, then the area of triangle pf1f2 is: (as long as the answer is good)
12. The equation of known curve is x ^ 2 / 16-y ^ 2 / 8 = 1, point P is on hyperbola, and the distance to one of focus F1 is 10, point P is on hyperbola And the distance to one of the focal points F1 is 10, and point n is the midpoint of Pf1. Find the size of / on / (o is the origin coordinate)
13. It is known that P is a point on the hyperbola X / 16-y / 9 = 1 with F1 and F2 as the focus, and the trajectory equation of the center of gravity g of △ f1f2p is obtained RT
14. It is known that F1 and F2 are the two focuses of the hyperbola x ^ 2 / 16 - y ^ 2 / 9 = 1, and P is a point on the hyperbola, It is known that F1 and F2 are two focal points of hyperbola x ^ 2 / 16 - y ^ 2 / 9 = 1, P is a point on hyperbola, and Pf1 ⊥ PF2. Find the area of △ pf1f2
15. The left and right focus of the hyperbola x2a2 − y2b2 = 1 is F1, F2, P is a point on the hyperbola, satisfying | PF2 | = | F1F2 |, and the straight line Pf1 is tangent to the circle x2 + y2 = A2, then the eccentricity e of the hyperbola is () A. 3B. 233C. 53D. 54
16. F 1 and F 2 are the focus of hyperbola, if there is P point in the right branch of hyperbola, which satisfies | PF2 | = | F1F2 | and F 1 and circle x ^ 2 + y ^ 2 = a ^ 2 F1 and F2 are the focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1. If the right branch of hyperbola has P point, satisfying | PF2 | = | F1F2 | and F1 is tangent to circle x ^ 2 + y ^ 2 = a ^ 2, then the asymptote equation of hyperbola is 4x±3y=0 Wrong number. Pf1 is tangent to the circle x ^ 2 + y ^ 2 = a ^ 2
17. Let the two focal points of the hyperbola be f 1. F 2. If | pf 2 | = 2 | f 1F 2 |, then the eccentricity of the hyperbola is zero
18. Given that P is a point on the right branch of hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1, F1 and F2 are the left and right focuses of hyperbola respectively If s △ mpf1 = s △ mpf2 + MS △ mf1f2 holds, then the value of M is
19. Hyperbola problem: F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), Given that F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), if there is a point a on the right branch, so that the distance between point F2 and straight line AF1 is 2a, then the value range of eccentricity of the hyperbola is Given that F1 and F2 are the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), if there is a point a on the right branch, so that the distance between point F2 and straight line AF1 is 2a, what is the range of eccentricity of the hyperbola
20. If the common focus of ellipse X225 + y216 = 1 and hyperbola x24 − Y25 = 1 is F1, F2, P is an intersection of two curves, then the value of | Pf1 | · | PF2 | is______ ．