"A = 3 or a = - 2" is the () condition that the line ax + 2Y + 3A = 0 and the line 3x + (A-1) y = A-7 are parallel and not coincident A. Sufficient and unnecessary B. necessary and not sufficient C. sufficient and necessary D. neither sufficient nor necessary

"A = 3 or a = - 2" is the () condition that the line ax + 2Y + 3A = 0 and the line 3x + (A-1) y = A-7 are parallel and not coincident A. Sufficient and unnecessary B. necessary and not sufficient C. sufficient and necessary D. neither sufficient nor necessary

According to the necessary and sufficient condition that two lines are parallel, a1b2-a2b1 = 0 (1) And a1c2-a2c1 ≠ 0 (2) Because {3} is a proper subset of {3, - 2}, a = 3 or a = - 2 "is a necessary and sufficient condition for {ax + 2Y + 3A = 0 and {3x + (A-1) y = A-7} to be parallel and not coincident

If the center of the circle C is on the straight line 5x-3y = 8 and the circle C is tangent to the coordinate axis, the equation of the circle is____

Let (x0, Y0) be the center of the circle and R be the radius
According to the center of the circle on 5x-3y = 8, the circle is tangent to the coordinate axis
5x0-3y0=8 (1)
|x0|=|y0| (2)
r=|x0| (3)
According to the slope of the straight line 5x-3y = 8, k = 5 / 3, B = - 8 / 3, the straight line passes through quadrant 1, 3 and 4, and the circle can only be judged in the fourth quadrant,
So we get: x0 > 0, Y0

The standard equation for a circle whose center is on a straight line 5x-3y = 8 and tangent to two coordinate axes

If x = y, then x = y = 4; if x = - y, then x = 1, y = - 1, then the center of the circle is (4,4) or (1, - 1) because the radius is the distance from the center of the circle to the tangent line, that is, the center of the circle is (4,4)