Given that points a (x1, Y1) and B (X2, Y2) are two moving points on the circle C1: (x-1) &# 178; + Y & # 178; = 4, O is the origin of coordinates and satisfies the vector OA * ob = 0, The circle whose diameter is ab is C2 (1) If the coordinate of point a is (3,0), find the coordinate of point B (2) Finding the trajectory equation of the center C2 (3) Finding the maximum area of circle C2

Given that points a (x1, Y1) and B (X2, Y2) are two moving points on the circle C1: (x-1) &# 178; + Y & # 178; = 4, O is the origin of coordinates and satisfies the vector OA * ob = 0, The circle whose diameter is ab is C2 (1) If the coordinate of point a is (3,0), find the coordinate of point B (2) Finding the trajectory equation of the center C2 (3) Finding the maximum area of circle C2

(1) Easy intersection of circle and Y axis (0,3), (0, - 3)
∵ OA ⊥ ob, a is on the x-axis
х B is
(2) Easy to get OC = 0.5ab
2(X^2+Y^2)=((X1-X2)^2+(Y1-Y2)^2)
2(X^2+Y^2)=(((X1-1)-(X2-1))^2+(Y1-Y2)^2)
Open the right side function, note that x1 · x2 + Y1 · y2 = 0 and (x1, Y1) (X2, Y2) is the point on the circle
The solution is x ^ 2-x + y ^ 2 = 2
(3) The distance between C and O is half of ab. to find the largest circle area is to find the longest OC
Is to find the maximum of x ^ 2 + y ^ 2
Let z = x ^ 2 + y ^ 2, which is a circle centered on O. the maximum value obtained from geometric knowledge is 7 / 4
The maximum area is 7 π / 4

Given that the points a (x1, Y1), B (X2, Y2) (x1x2 ≠ 0) are two moving points on the parabola y2 = 4x, O is the origin of the coordinate, the vectors OA and ob satisfy OA &; ob = 0, then the line AB passes through the fixed point

In the sector OAB, the angle AOB = 60 degrees, C is a moving point on the arc AB (not coincident). If OC vector = xoa vector + yob vector, μ = x + py (P > 0) has a maximum value, the value range of P is obtained?

As shown in the figure, let ∠ COA = θ, then 0 ° & lt; θ & lt; 60 °. Let | OA | = | ob | = | OC | = R (R & gt; 0), OA * ob = 1 / 2 * R ^ 2, so OC * OA = | OC | * | OA | * cos θ, that is, X * R ^ 2 + 1 / 2 * y * R ^ 2 = R ^ 2 * cos θ, thus x + 1 / 2 * y = cos θ, similarly, OC * ob = | OC | * | ob | * cos (...)