Given that P is any point of the circle C: x ^ 2 + y ^ 2 + 4x + ay-5 = 0, the symmetric point of P about 2x + Y-1 = 0d is still on the circle

Given that P is any point of the circle C: x ^ 2 + y ^ 2 + 4x + ay-5 = 0, the symmetric point of P about 2x + Y-1 = 0d is still on the circle

The symmetric point of any point on the circle C with respect to the line 2x + Y-1 = 0 is on the circle C,
Then the line 2x + Y-1 = 0 passes through the center of the circle
SO 2 × (- 2) + (- A / 2) - 1 = 0
a=－10

If we know that any point on the circle C: x ^ 2 + y ^ 2 + BX + ay-3 = 0 (a, B are positive real numbers) with respect to the symmetric point of the line L: x + y + 2 = 0 is on the circle C, then 1 / A + 3 / B is
Given that any point on the circle C: x ^ 2 + y ^ 2 + BX + ay-3 = 0 (a, B are positive real numbers) is symmetric with respect to the line L: x + y + 2 = 0, then the minimum value of 1 / A + 3 / B is? I already know the answer, what I want is the finer the process, the better

Obviously, from the meaning of the question, we know that the straight line L passes through the center of circle C (- B / 2, - A / 2), and substituting it into a + B = 4, then 1 / A + 3 / b = 1 / 4 (a + b) (1 / A + 3 / b) = 1 / 4 (1 + 3A / B + B / A + 3) ≥ 1 / 4 (4 + 2 √ 3)
The minimum value is obtained

Given that point P is any point on the circle C: x + 4x + ay-5 = 0, the symmetric point of point P about the line 2x + Y-1 = 0 is also on the circle C, a =?

From the meaning P in the circle C,
The symmetric point of point P about the line 2x + Y-1 = 0 is also on the circle C
We can get 2x + Y-1 = 0 over the center of the circle
Circle C: X & # 178; + 4x + Y & # 178; + ay-5 = 0
(x+2)²+(y+a/2)²=9+a²/4
The center of the circle is (- 2, - A / 2)
Substituting into the linear equation 2x + Y-1 = 0
A = - 10 can be obtained

It is known that the symmetric point of any point on the circle X & # 178; + Y & # 178; + BX + ay-3 = 0 (a, B are real numbers) with respect to the line L: x + y + 2 = 0 is on the circle C,
Find the value of 1 / A + 3 / b
It is easy to know that the center of the circle (- B / 2, - A / 2) is substituted by X + y + 2 = 0 to get a + B = 4
∴ √(ab)≤2 1/a+3/b=(b+3a)/ab≥2√（3ab）/ab
Substituting the minimum value √ 6
It is wrong, but 1 / 4 (a + b) = 1 multiplied by 1 / A + 3 / b. why

If and only if B = 3A and a + B = 4, the solution is a = 1, B = 3 and 1 / 4 (a + b) (1 / A + 3 / b) = 1 / 4 (4 + B / A + 3A / b) = 1 + 1 / 4 (B / A + 3A / b) ≥ 1 + 1 / 4