Given that the equation x + Y-2 (M + 3) x + 2 (1-4m) y + 16m + 9 = 0 represents a circle, find the value range of real number M

Given that the equation x + Y-2 (M + 3) x + 2 (1-4m) y + 16m + 9 = 0 represents a circle, find the value range of real number M

X2 + y2-2 (M + 3) x + 2 (1-4m2) y + 16m2 + 9 = 0, so (x-m-3) ^ 2 + (y + 1-4m ^ 2) ^ 2 = - 7m ^ 2 + 6m + 1, because - 7m ^ 2 + 6m + 1 > 0, so the range of m is (- 1 / 7,1). Please accept the answer
① If there are six straight lines intersecting each other on the plane, and only three of them pass through a point, the line segments that they cut each other without overlapping share ()
A. Clause 24 c.33 D
② C is a point on the segment AB, D is the midpoint of the segment CB. Given that the sum of all segments on AB is 23, the length of segment AC and the length of segment CB are positive integers, then the length of segment AC is ()
③ If three lines intersect each other and are not at the same point, then there are () equidistant points to the three lines
④ If there are three definite non collinear points a, B, C and a straight line L on the plane satisfying the condition that the distances between a, B and L are equal and equal to two times of the distance between C and l, then there are () such straight lines
⑤ There is a point P and a straight line L on the plane, and the distance between the point P and the straight line L is 3. Take P as the center of the circle and R as the radius to draw a circle. If the distance between two points on the circle and the straight line is equal to 2, find the range of radius R
⑥ There are 2002 straight lines A1, A2,... In the same plane A2002, if A1 is vertical A2, A2 is parallel A3, A3 is vertical A4, A4 is parallel A5 So the positional relationship between A1 and A2002 is ()
⑦ If there are six straight lines on the plane, only three of them intersect at a point, and the other three are parallel to each other, then the six straight lines divide the plane into () parts
1. D. draw three straight lines passing through the same point first, and then draw another three lines. Note: the last three lines must intersect any line drawn in front, for example, the fifth line must intersect all four lines in front
2.3.23=AB+AC+CB+AD+CD+DB=3AB+CD.
Let AB be x, then 3x + CD = 23
CD = 23-3 × 7 = 2, CB = 2 × 2 = 4, AC = 7-4 = 3
3.4. This point is the inner part of the triangle surrounded by three straight lines (i.e. the intersection of the bisectors of the three inner angles) plus three side centers (see the answer on the second floor, I was really wrong at the beginning)
4.2. One is between AB and C, and the other is outside point C
Five point one
The others are the same as the friends on the first floor. They only correct question (5). The correct answers are four. In fact, it is the triangle line of three side hearts plus one heart, a total of four. The side center is the center of the circle which is tangent to both sides of the triangle line and the third side. The side center is outside the triangle.
Two equations 1: x-3 / 5x = 5 / 6 2: 6 times 1 / 12-1 / 2x = 1 / 2 urgent! Thank you
1: X-3 / 5 x = 5 / 6 multiply both sides by 30 to get 30x-18x = 25 12x = 25 x = 25 / 12
X = 2 and 1 / 12
2: : 6 × 1 / 12-1 / 2 x = 1 / 2 1 / 2-1 / 2 x = 1 / 2, both sides multiply by 2 to get:
1-X=1 X=0 .
Let's know the equation 4x (unknowns) minus 1 equals 3x (unknowns) minus 2A (unknowns) and 3x (unknowns) minus 1 equals 6x (unknowns) minus 2A (unknowns)
It's hard
Find the value of A
4X-1=3X-2A
3X-1=6X-2A
You only give the conditions, what do you want?
A and X
If it is
Combine these two equations
Just simplify it
X=1-2A
3X=2A-1
Solution
A=1/2
X=0
4x-1=3x-2a;(1)
3x-1=6x-2a;(2)
(2)-(1):
-x=3x;=>x=0;
Given the equation x ^ 2 + y ^ 2-2 (M + 3) X-2 (1-4m ^ 2) y + 16m ^ 4 + 9 = 0, if the equation represents a circle, find the value range of M and the locus of the center of the circle
I've worked out the range of M. if I'm not wrong, it should be - 1 / 7
The landlord's calculation may be wrong
The equation can be reduced to
[x-(m+3)]^2+[y-(1-4m^2)]^2=-(7m+1)(m-1)
If and only if - 1 / 7
Let's know x + y = - 3, the third power of X + the third power of y = - 18, how much is the seventh power of X + the seventh power of y equal to?
x^3+y^3=(x+y)(x^2-xy+y^2)
(x^2-xy+y^2)=(x^3+y^3)/(x+y)=-18/(-3)=6
(x+y)^2=x^2+2xy+y^2=(x^2-xy+y^2)+3xy
(-3)^2=6+3xy
xy=1
(x^3+y^3)*(x+y)^2=x^5+y^5+2*x^4*y+2*x*y^4+x^3*y^2+x^2*y^3
=(x^5+y^5)+2xy(x^3+y^3)+x^2*y^2*(x+y)
=(x^5+y^5)-36-3
x^5+y^5=(-18)*(-3)^2+36+3=-123
(x^3+y^3)^2*(x+y)=x^7+2*x^4*y^3+x*y^6+y^7+2*x^3*y^4+x^6*y
=(x^7+y^7)+(2*x^4*y^3+2*x^3*y^4)+(x*y^6+x^6*y
)
=(x^7+y^7)+2*(x^3*y^3)(x+y)+xy(x^5+y^5)
=(x^7+y^7)-6-123
x^7+y^7=(-18)^2*(-3)+6+123=-843
x^3+y^3
=(x+y)(x^2-xy+y^2)
=(x+y)[(x+y)^2-3xy]
=(x+y)^3-3xy(x+y)
=-27+9xy=-18
xy=1
x^7+y^7
=(x^3+y^3)(x^4+y^4)-x^3y^4-x^4y^3
=-18(x^4+y^4)-x^3y^3(x+y)
=-18(x^4+y^4)+3
x^4+y^4=(x^3+y^3)(x+y)-x^3y-xy^3
=54-(x^2+y^2)
=54-[(x+y)^2-2xy]
=54-(9-2)
=47
x^7+y^7=-18*47+3=-843
x^3+y^3
=(x+y)(x^2-xy+y^2)
=(x+y)[(x+y)^2-3xy]
=(x+y)^3-3xy(x+y)
=-27+9xy=-18
xy=1
x^7+y^7
=(x^3+y^3)(x^4+y^4)-x^3y^4-x^4y^3
=-18(x^4+y^4)-x^3y^3(x+y)
=-18 (x ^ 4 + y ^ 4)... Expand
x^3+y^3
=(x+y)(x^2-xy+y^2)
=(x+y)[(x+y)^2-3xy]
=(x+y)^3-3xy(x+y)
=-27+9xy=-18
xy=1
x^7+y^7
=(x^3+y^3)(x^4+y^4)-x^3y^4-x^4y^3
=-18(x^4+y^4)-x^3y^3(x+y)
=-18(x^4+y^4)+3
x^4+y^4=(x^3+y^3)(x+y)-x^3y-xy^3
=54-(x^2+y^2)
=54-[(x+y)^2-2xy]
=54-(9-2)
=47
x^7+y^7=-18*47+3=-843
OK, put it away
-843
Fill in the blanks (1) 5 square meters 80 square decimeters = () square decimeters (2) in 3.5 + X, 6 + 5x
1、580
2、8X-5X=2.4
3、828
4、2.8
5、32.3
6、4X+24
7、7.84
Let the range of X be meaningful
1. Radical 3-2x
Root sign of 2x 2 + 1
The base number under the root sign is called the base number. To make the root meaningful, the base number must be meaningful and greater than or equal to 0
In 1, X should be less than or equal to 3 / 2
2, because 2x + 1 is the denominator, so x cannot be equal to - 1 / 2, and the range of X is that x is greater than - 1 / 2
1,3-2x>=0
2x-1
x>-1/2
1. Just 3-2x > = 0
2. 2X + 1 > 0 (cannot be 0 because it is on the denominator)
1.3-2X>=0, X0, X>-1/2
The known equation x & # 178; + Y & # 178; - 2x-4y + M = 0
(1) If the equation represents a circle, find the range of M;
(2) If the circle and line in (1) intersect at M and N, and OM ⊥ on, the value of M is obtained;
(3) If the circle and the line in (1) intersect at two points m and N, the equation of circle with diameter Mn is obtained
(1) X & # 178; + Y & # 178; - 2x-4y + M = 0, that is, (x-1) &# 178; + (Y-2) &# 178; = 5-m. if this equation represents a circle, then 5-m ﹥ 0 ﹥ m ﹤ 5
 
(1) When the temperature increases by 1 ° C, the length of a wire is 0.002mm. Conversely, when the temperature decreases by 1 ° C, the wire is shortened by 0.002mm. The wire at 15 ° C is heated to 60 ° C, and then cooled to 5 ° C. what is the change in the length of the wire? How much is the final length longer than the original length?
(2) In a year, the distance between the earth and the sun changes with time. One astronomical unit is the average distance between the earth and the sun, which is 149.6 million kilometers. How many square meters is an astronomical unit expressed by scientific counting method?
(1) When the temperature increases by 1 ° C, the length of a wire is 0.002mm. On the contrary, when the temperature decreases by 1 ° C, the wire is shortened by 0.002mm. The wire at 15 ° C is heated to 60 ° C, and then cooled to 5 ° C. what is the change in the length of the wire? How much is the final length longer than the original length