It is known that a focus of hyperbola is (- 4,0), and the equation of an asymptote is 2x-3y = 0 I'm in a hurry

It is known that a focus of hyperbola is (- 4,0), and the equation of an asymptote is 2x-3y = 0 I'm in a hurry

∵C＝4,b／a＝2／3
And C ＾ 2 = a ＾ 2 + B ＾ 2
∴16＝a＾2＋4a＾2／
A ＾ 2 = 144 / 13, B ＾ 2 = 64 / 13
The hyperbolic equation is x ＾ 2 / 144 / 13 - y ＾ 2 / 64 / 13 = 1
As shown in the figure, the asymptote of hyperbola C is 2x ± 3Y = 0, and the distance between two vertices is 6
When the focus is on the x-axis, the asymptote of hyperbola C1 is 2x ± 3Y = 0, Ba = 23, the distance between two vertices is 6, a = 3, B = 2, the equation of hyperbola is x29-y24 = 1. When the focus is on the y-axis, the asymptote of hyperbola C1 is 2x ± 3Y = 0, ab = 23. The distance between two vertices is 6, a = 3
It is known that the center of hyperbola C is at the origin, the focus is on the x-axis, the distance between point P (- 2.0) and its asymptote is √ 10 / 5, the straight line passing through point P with a slope of 1 / 6 intersects the hyperbola at two points a and B, intersects the y-axis at m, and PM is the equal proportion of PA and Pb
(1) Find the asymptote equation of hyperbola C;
(2) Find the equation of hyperbola C
It takes a lot of time to calculate and type, and we hope to adopt it. If we don't set up the linear parameter equation, the amount of calculation will be huge. We must learn this method
The square root of 3 / 10 + 2 and 3 / 5 are estimated and compared!
The square root of 3 / 10 + 2 is greater than 1, and 3 / 5 is less than 1
So the square root of 3 / 10 + 2 is greater than 3 / 5
3 / 10 + 2 means 23 / 10 is greater than 1, so the square root is greater than 1;
And 3 / 5 is less than 1, so the square root of 3 / 10 + 2 is greater than 3 / 5
Let's not say 3 / 10, the square root of 2 is greater than 1, definitely greater than 3 / 5
3 / 10 + 2 is definitely more than 3 / 5
If α and β are the two real roots of the equation x ^ 2-2ax + A + 6 = 0, then the minimum value of (α - 1) ^ 2 + (β - 1) ^ 2 is______ .
RT.
By using Weida's theorem, α + β = 2A, α β = a + 6 (α - 1) ^ 2 + (β - 1) ^ 2 = α + β - 2 (α + β) + 2 = (α + β) - 2 α β - 2 (α + β) + 2 = 4a-4a-2a-12 + 2 = 4a-6a-10, and because there are real roots △≥ 0, 4a-4a-24 ≥ 0, a-a-6 ≥ 0, a ≤ - 2 or a ≥ 3, when a = 3, the minimum value of 4a-6a-10 is 8, so the minimum value of (α - 1) ^ 2 + (β - 1) ^ 2 is 8
Remember to adopt it
Five
How to solve the equation of 8x-56 / 1.4 = 70.4
8X-56/1.4=70.4
8x-40=70.4
8x=70.4+40
8x=110.4
x=13.8
8X-56/1.4=70.4
8x-40=70.4
8x=110.4
x=13.8
Solution 8x = 70.4 + 56 / 1.4
8X=110.4
X=110.4/8
X=13.8
8x-56/1.4=70.4
8x=110.4
x=13.8
On the comparison of square root estimation
Compare the size of √ 10-1 and 2
Compare the size of √ 6 and 2.5
Please explain the process of getting big and small conclusions!
It's not an accurate calculation, it's just an estimate of size~
√10-1>√9-1=2
So √ 1
√6
10> 9,10 ^ (1 / 2) > 9 ^ (1 / 2), that is, 10 ^ (1 / 2) > 3
So 10 ^ (1 / 2) - 1 > 2
Six
If the equation x & # 178; - 2ax-1 = 0 has two different roots, α and β satisfy - 1 respectively
Let f (x) = x ^ 2-2ax-1
According to the position of the two points, four inequalities can be obtained
F (- 1) > 0, i.e. 1 + 2a-1 > 0, a > 0
f(0)
Let f (x) = x & # 178; - 2ax-1
There are two different roots α and β satisfying - 1, respectively
Solve the equation. Kneel to find x plus 1.8x equals 0.56
x+1.8x=0.56
2.8x=0.56
x=0.56/2.8
x=0.2
x+1.8x=0.56
2.8x=0.56
x=0.56÷2.8
x=0.2
Do not understand can ask, help please adopt, thank you!
X plus 1.8x equals 0.56
2.8x=0.56
x=0.56÷2.8
x=0.2
x+1.8x＝0.56
2.8x＝0.56
x＝0.2
By estimation, compare the square root of 6 with the size of 2.5
Because the square of the root 6 equals 6
The square of 2.5 equals 6.25
So 6 < 6.25
So root 6 is less than 2.5
2.5, you square the two numbers separately and then compare them
Then compare the size of 6 and 2.5 square. 6 is less than 6.25, so 2.5 is greater than root 6