The position relationship of straight line and circle (15 17:25:7) Solve the equation of the circle with the smallest area and the intersection of the line 2x + y + 4 = 0 and the circle x2 + Y2 + 2x-4y = 0

The position relationship of straight line and circle (15 17:25:7) Solve the equation of the circle with the smallest area and the intersection of the line 2x + y + 4 = 0 and the circle x2 + Y2 + 2x-4y = 0

According to the two formulas, the coordinates of the two intersections are obtained
(- 3,2) and (- 11 / 5,2 / 5)
Get the length and midpoint coordinates of the line segment connected by two points
The length is 4 (root 10) / 5
The midpoint coordinates are (- 13 / 5,2 / 5)
Taking the midpoint as the center of the circle and the length of the line as the diameter, the circle formula is obtained
(x+13/5)^2 + (y-2/5)^2 = 8/5
How to solve the problem:
See "crossing the intersection of line 2x + y + 4 = 0 and circle x square + y square + 2x-4y + 1 = 0"
You should think that you will get the coordinates of two intersections by calculation
And see the "equation of the smallest circle"
What kind of circle do you want to think of that has the smallest area
The answer is the circle with the smallest radius
The next step is what kind of circle has the smallest radius of two known intersections
That's when the line between the two constant points is the diameter of the circle
So it is not difficult to work out the above calculation

Find the maximum and minimum of the function y = (2-sina) / (2-cosa)

Let k = (2-sina) / (2-cosa)
So K is the slope of the line passing through two points a (2,2) and B (COSA, Sina)
sin²a+cos²a=1
So B is on the unit circle
At the same time, B is on the line ab
So the line and the circle share the same point
So the distance from the center of the circle (0,0) to the straight line Y-2 = K (X-2) is less than or equal to the radius r = 1
kx-y+(2-2k)=0
So the distance = | 0-0 + 2-2k | / radical (k ^ 2 + 1)

If α and β belong to (0, half) and cos α = 0.6, cos (α + β) = - 5 / 13, the values of COS (2 α + β) and Cos2 β are obtained

Cos α = 0.6, so sin α = 0.8, cos (α + β) = - 5 / 13, so sin (α + β) = 12 / 13
cos（2α+β）=cos(α+α+β)=cosαcos(α+β)-sinαsin(α+β)
=0.6*（-5/13）-0.8*（12/13）
=-63/65

One third of a number is the reciprocal of seven thirds. Find the number

Let this number be X
The reciprocal of seven out of three is three out of seven
One third x = three seventh
X = three seventh divided by one third
X = nine out of seven