The straight line passing through the point P (- 2,3) is cut by the circle X & sup2; + Y & sup2; - 4x + 2y-2 = 0, and the linear equation of the longest chord is obtained | Math enthusiast | Mathematical art

The straight line passing through the point P (- 2,3) is cut by the circle X & sup2; + Y & sup2; - 4x + 2y-2 = 0, and the linear equation of the longest chord is obtained

x²+y²-4x+2y-2=0
（x-2）²+（y+1）²=7
Then the longest string passes through the center of the circle (2, - 1)
The equation of the line
y-3=(3+1)/(-2-2)*(x+2)
y-3=-(x+2)
x+y=1

Given the circle x2 + Y2 + KX + 2Y + K2 = 0, when the area of the circle is the maximum, the center coordinate is ()
A. （0，-1）B. （1，-1）C. （-1，0）D. （-1，1）

According to the meaning of the topic, the center coordinate of the circle is (- K2, - 1), and the radius of the circle is r = 124 − 3k2. In order to maximize the area of the circle, that is, the radius r of the circle is the maximum value, so when k = 0, r takes the maximum value of 1, and the center coordinate of the circle is (0, - 1)

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The straight line passing through the point P (- 2,3) is cut by the circle X & sup2; + Y & sup2; - 4x + 2y-2 = 0, and the linear equation of the longest chord is obtained