The maximum distance from the point on x ^ 2 + y ^ 2-2x + 4Y + 4 = 0 to the line 3x-4y + 9 = 0 is equal to?

The maximum distance from the point on x ^ 2 + y ^ 2-2x + 4Y + 4 = 0 to the line 3x-4y + 9 = 0 is equal to?

Formula 1 is a circle with a circle point of (1, - 2) and a radius of 1. The maximum distance between a line and a circle is the distance from the center of the circle to the line plus the radius, so just find the distance between the point (1, - 2) and the line
5. The distance from the center of the ball to the straight line first, and then the radius
solution
x^2+y^2-2x+4y+4=0
(x-1)^2+(y+2)^2=1
The center of the circle is (1, - 2) and the radius is r = 1
The distance from the center of the circle to the straight line is:
d=|3+8+9|/√3^2+4^2=20/5=4
The center of the circle is separated from the straight line
The maximum distance is: 4 + r = 4 + 1 = 5
1. Real numbers a, B, C satisfy (a + C) (a + B + C) < 0, and prove: (B-C) & sup2; > 4a (a + B + C)
2. It is known that the vertex coordinates of the parabola y = ax & sup2; + BX + C are (2,4), (1) if the intersection points of the straight line y = KX + 4 (K ≠ 0), the Y-axis and the parabola are D, e, F, and s △ respectively ODE:S Δ OEF = 1:3, where o is the origin of the coordinate, and K (2) is expressed by the algebraic formula containing A. if the length of the line segment EF satisfies the condition of 3 radical 2 ≤ m ≤ 3 radical 5, the value range of a is determined
This, the second question can not download ah
1. ∵ (a+c)(a+b+c)0,(a+b+c)0,(a+b+c)
Division of rational numbers
（-0.25）÷（-1.3）
12÷（-1\3）÷1\2
（-7）÷（-7）÷0.1
(- 2.75) / (4 and 2 / 5) / (- 4 / 5)
（-2）÷[（-1\3）÷（-4）]
The room temperature of a fruit cold storage is - 2 ° C. now a batch of fruits are stored at 10 ° C. if the temperature of the cold storage can be raised by 3 ° C per hour, then all the required temperatures can be reached in a few hours
The difference between 10 ° C and - 2 ° C is 12 ° C. the temperature of cold storage rises to 3 ° C in 1 hour and 12 ° C in 4 hours
10-（-2）÷3=4
The difference between 10 ° C and - 2 ° C is 12 ° C. the temperature of cold storage rises to 3 ° C in 1 hour and 12 ° C in 4 hours
10 - (- 2) △ 3 = 4 question: (- 0.25) / (- 1.3) 12 ^ (- 1 / 3) ^ (- 1 / 2 (- 7) ^ (- 7) ^ (- 0.1 (- 2.75) ^ (4 and 2 / 5) ^ (- 4 / 5) (- 2) ^ [(- 1 / 3) ^ (- 4)]
The distance from point a (6,4) to line 4y-3x + 1 = 0 is equal to?
1/5
Verification: 4A ^ 2 + B ^ 2 ≥ 2B (a + 3) + 2A (B-6) - 9, where a and B are real numbers
Left right
=4a^2+b^2-4ab+12a-6b+9
=(2a-b)^2+6(2a-b)+9
=(2a-b+3)^2
>=0
Left > = right
Left right
=4a^2+b^2-4ab+12a-6b+9
=(2a-b)^2+6(2a-b)+9
=(2a-b+3)^2
>=0
Left > = right
Simple operation of rational division in the first semester of junior high school
For the simplest operation
① (- 11) × (two fifths) + (- 11) × 2 and two fifths + (- 11) × (- one fifths)
② (- 98) × (- 0.125) + (- 98) × 1 / 8 - 98 × (- 4 / 7)
I want the easiest one, and I have to say both questions. I'll give you 10 more points
1. Because every term has a - 11, so put it forward - 11 × (2 / 5 + 2 / 5 - 1 / 5) = - 11 × (13 / 5) = - 143 / 5
2. We also put forward - 98, so the original formula = - 98 × (- 0.125 + 1 / 8-4 / 7) = 392 / 7
Given that X and y satisfy the conditions 2x + 5Y ≥ 10,2x-3y ≥ - 6,2x + y ≤ 10 at the same time, the value range of Y + 1 / x + 1 is obtained
Linear programming, draw the feasible region, and then,
The key to this problem is that the formula (y + 1) / (x + 1) represents the slope of the line between the point (x, y) and the fixed point (- 1, - 1) in the feasible region;
Go and draw by yourself. You should know it. Draw it. The maximum slope point is (0,2). At this time, (y + 1) / (x + 1) = 3;
The minimum point of slope is (5,0), where (y + 1) / (x + 1) = 1 / 6
Therefore, the value range of Y + 1 / x + 1 is: [1 / 6,3]
The key is to connect the slope formula, and we will encounter the distance formula between two points in the future, such as (x + 1) ^ 2 + (y + 1) ^ 2
This is the square of the distance between the point (x, y) in the feasible region and the fixed point (- 1,1);
If you don't understand, please hi me,
Let a, B and C be positive real numbers, and find the minimum of a / B + 2C + B / C + 2A + C / A + 2B
Using Cauchy Inequality: [a (B + 2C) + B (c + 2a) + C (a + 2b)] × [A / (B + 2C) + B / (c + 2a) + C / (a + 2b)] ≥ (a + B + C) ^ 2 (in fact, it is to multiply by 3AB + 3bC + 3CA) a, B and C are all positive numbers, so a / (B + 2C) + B / (c + 2a) + C / (a + 2b) ≥ (a + B + C) ^ 2 / (3AB + 3bC + 3CA) ∵
The first: 0 △ 0.12, the second, (- 0.5) △ 1 / 4, the third, (- 1.25) divided by 1 / 4
The fourth, 4 / 7 divided by (- 12), the fifth, (- 378) / - 7) / - 9
The sixth, (- 0.75) × 5 / 4 △ 0.3) the seventh, (- 3.2) × 96 / 5
8, (- 9 / 14) △ 2.5 I'm in a hurry. Brothers and sisters, please do me a favor. Thank you. The sooner the better. Thank you
1·0÷（0·12）＝0
2·（－0·5）÷（－1／4）
＝（－0·5）÷（－0·25）
＝2
3·（－1·25）÷（1／4）
＝（－1·25）÷（0·25）
＝－5
4·（4／7）÷（－12）
＝（4／7）×（－1／12）
＝－1／21
5·（－378）÷（－7）÷（－9）
＝54÷（－9）
＝－6
6·（－0·75）÷（5／4）÷（－0·3）
＝（－0·75）÷（1·25）÷（－0·3）
＝（－0·6）÷（－0·3）
＝2
7·（－3·2）÷（96／5）
＝（－16/5）÷（96／5）
＝（－16／5）×（5／96）
＝－1／6
8·（－9／14）÷2·5
＝（－9／14）÷（35／14）
＝（－19／14）×（14／35）
＝－19／35
1. Any number = 0
2、（-1/2）÷（-1/4）=2
3、（-5/4）÷1/4=-5
4、4/7÷（-12）=4/7*（-1/12）=-1/21
5、（-378）÷63=-6
6、（-3/4）*4/5*10/3=2
7、（-16/5）*5/96=1/6
8、（-9/14）*2/5=-9/35
In the middle is about
1·0÷（0·12）＝0
2·（－0·5）÷（－1／4）
＝（－0·5）÷（－0·25）
＝2
3·（－1·25）÷（1／4）
＝（－1·25）÷（0·25）
＝－5
4·（4／7）÷（－12）
＝（4／7）×（－1／12）
＝－1／21
5·（－378）÷（－7）÷（－9）
＝54÷（－9）
Given that X and y satisfy the conditions 2x + 5Y ≥ 10,2x-3y ≥ - 6,2x + 2Y ≤ 10 at the same time, finding the value range of Y + 1 / x + 1 is necessary
（1/6,3）
[1/6,3]