It is known that the center of circle C and point P (- 2,1) are symmetric with respect to the line y = x + 1. The line 3x + 4y-11 = 0 intersects circle C at two points a and B, and | ab | = 6, then the equation of circle C is______ ．

It is known that the center of circle C and point P (- 2,1) are symmetric with respect to the line y = x + 1. The line 3x + 4y-11 = 0 intersects circle C at two points a and B, and | ab | = 6, then the equation of circle C is______ ．

Let C (a, b) be the center of the circle. According to the symmetry of the center of the circle and P with respect to the line y = x + 1, the line CP is perpendicular to y = x + 1, and the slope of y = x + 1 is 1, so the slope of the line CP is - 1, that is, 1 − B − 2 − a = - 1 is reduced to a + B + 1 = 0 (1), and then according to the midpoint of CP on the line y = x + 1, 1 + B2 = a − 22 + 1 is reduced to a-b-1 = 0 (2), a = 0 (2), B = - 1 is obtained simultaneously (1), so the coordinates of the center of the circle are (0, - 1) The distance of straight line AB d = | - 4 − 11 | 32 + 42 = 3, 12 | ab | = 3, so according to the Pythagorean theorem, the radius R2 = 32 + (− 4 − 11) 252 = 18, so the equation of circle is x2 + (y + 1) 2 = 18. So the answer is: x2 + (y + 1) 2 = 18

Calculate the following questions: [2 / 3x & # 178; - 2 / (X & # 178; + Y & # 178;) times (X & # 178; + Y & # 178;) / 3x & # 178; - X & # 178; - Y & # 178;)]

2/3x²-2/(x²+y²)*(x²+y²)/3x²-x²-y²
=2/3x²-2/3x²-x²-y²
=-x²-y²
Is your formula like this?

Given 3x + 2 = 0, then x ^ + 2x + 1 = how much

3X+2=0
x=-2/3
x^+2x+1
=4/9-4/3+1
=1/9