Mathematics problems of senior one (equation of circle) The known curve C: X & # 178; + Y & # 178; - 4ax + 2ay + 10A-5 = 0 (1) Verification: no matter what the value of a is, the curve C must pass the fixed point; (2) When a ≠ 1, we prove that the curve C is a circle, and the center of the circle is on a straight line; (3) If the curve C is tangent to the Y axis, find the value of A

Mathematics problems of senior one (equation of circle) The known curve C: X & # 178; + Y & # 178; - 4ax + 2ay + 10A-5 = 0 (1) Verification: no matter what the value of a is, the curve C must pass the fixed point; (2) When a ≠ 1, we prove that the curve C is a circle, and the center of the circle is on a straight line; (3) If the curve C is tangent to the Y axis, find the value of A

(x ^ 2 + y ^ 2-5) + 2A (- 2x + y + 5) = 0x ^ 2 + y ^ 2-5 = 0-2x + y + 5 = 0, y = 2x - 55x ^ 2-20x + 20 = 0x ^ 2-4x + 4 = 0, x = 2, y = - 1 no matter what value a takes, the curve C must pass through a fixed point, and the fixed-point coordinates (2, - 1) curve C: X & # 178; + Y & # 178; - 4ax + 2ay-5 + 10A = 0 (x-2a) ^ 2 + (y + a) ^ 2 = 5A ^ 2-10a + 5 = 5 (A-1) ^ 2A

Judge whether the following equation represents a circle, if so, turn it into a standard equation. (1) x2 + Y2 + 2x + 1 = 0 (2) x2 + Y2 + 2ay-1 = 0 (3) x2 + Y2 + 20x + 121 = 0 (4) x2 + Y2 + 2aX = 0
X2 is the square of X, Y2 is the square of Y, and 2x is 2 times X

(1) (x + 1) ^ 2 + y ^ 2 = 0, not a circular equation
(2) X ^ 2 + (y + a) ^ 2 = 1-A ^ 2, when - 1

Find the equation of the circle tangent to y = x through the intersection of the line x + y + 4 = 0 and the circle x ^ 2 + y ^ 2 + 4x-2y-4 = 0

Let the circular equation be: x2 + Y2 + 4x-2y-4 + λ (x + y + 4) = 0
∴ 2x2＋(2＋2λ)x＋4λ－4＝0
Let Δ = 0 (2 + 2 λ) 2-4 × 2 × (4 λ - 4) = 0, the solution: λ = 3
So the equation of circle is x2 + Y2 + 7x + y + 8 = 0

1. Let real numbers x and y satisfy 2x + (Y-1) 2 = 1, and find the maximum of the following formulas
(1)3X+4Y
(2)X^2+Y^2
(3)Y+2/X+1
2 solve the equation of a circle which satisfies one of the following conditions and the intersection of the line 2x + y + 4 = 0 and the circle x ^ 2 + y ^ 2 + 2x-4y + 1 = 0
(1) Over origin
(2) There is a minimum area

If you are a freshman in high school, you may not have learned some things. Let me tell you first. If you have any problems, please send me a message 1. The image is a parabola with (1 / 2, - 1) as its vertex and y = - 1 as its axis of symmetry