Ask for help high school "basic inequality" problem: known circle C: the square of X + the square of Y + BX + ay-3 = 0 (a, B are positive real numbers) on any point about the straight line L: 1 Given that any point on the circle C: x square + y square + 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 the minimum value of 1 / A + 3 / B is___ .

Ask for help high school "basic inequality" problem: known circle C: the square of X + the square of Y + BX + ay-3 = 0 (a, B are positive real numbers) on any point about the straight line L: 1 Given that any point on the circle C: x square + y square + 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 the minimum value of 1 / A + 3 / B is___ .

Any point on the square of X + the square of Y + BX + ay-3 = 0 (a, B are positive real numbers) with respect to the symmetry point of the line L: x + y + 2 = 0 is on the circle C, which means that the line l must be known by the equation of the circle through the center of the circle, and the coordinates of the center of the circle are (- B / 2, - A / 2) + 2 = 0, a + B = 41 / A + 3 / b = (1 / 4) * 4 (1 / A + 3 / b) = (1 / 4) (a + b) (1 / 4)

Given that any point on the circle x2 + Y2 + BX + ay-3 = 0 (a > 0, b > 0) with respect to the symmetry point of the line L: x + y + 2 = 0 is on the circle C, then the minimum value of a / 1 + B / 1 is

From the equation of the circle, we know that the center of the circle is (- A / 2, - B / 2), there is: - A / 2-B / 2 + 2 = 0, that is: A / 2 + B / 2 = 2, but you may have a wrong number, which may require 1 / A + 1 / b (otherwise it is a fixed value). If so, it is not equal to Cauchy

If the area of circle x ^ 2 + y ^ 2 + 2x + ay-a-12 = 0 is the smallest

The equation x & # 178; + Y & # 178; + 2x + ay-a-12 = 0 is formulated to (x + 1) &# 178; + (y + A / 2) &# 178; = A & # 178; / 4 + A + 13,
Then R & # 178; = A & # 178 / 4 + A + 13 = (a + 2) &# 178 / 4 + 12,
When a = - 2, (R & # 178;) min = 12, that is, (R) min = 2 √ 3,
In this case, the minimum area of the circle is 12 π