The line L passing through the focus f on the ellipse 2x ^ 2 + y ^ 2 = 2 intersects the ellipse at two points a and B to find the maximum area of Δ AOB (o is the origin) The answer is only √ 2 / 2. Is there anything wrong in it? Or is the answer wrong There's a wrong step in the middle. Oh, forget it

2X^2+Y^2=2
x^2+y^2/2=1
a^2=2,b^2=1,c^2=a^2-b^2=1,c=1
Let f (0,1) be the focus
Linear l equation: y = KX + 1
Coordinate of intersection with X axis: C (- 1 / K, 0)
Take y = KX + 1 generation: 2x ^ 2 + y ^ 2 = 2 to get:
2x^2+(kx+1)^2=2
(2+k^2)x^2+2kx-1=0
x1+x2=-k/(2+k^2),x1x2=-1/(2+k^2)
(x1-x2)^2=(x1+x2)^2-4x1x2=(5k^2+8)/(2+k^2)^2
(y1-y2)^2=k^2(x1-x2)^2=k^2(5k^2+8)/(2+k^2)^2
Δ AOB area s
=|The abscissa of point y1-y2 | * | C | * 1 / 2
=√(5k^2+8)/2(2+k^2)
4S^2(2+k^2)^2=5k^2+8
4S^2k^4+(16S^2-5)k^2+16S^2-8=0
Discriminant △ = (16S ^ 2-5) ^ 2-4 * 4S ^ 2 (16S ^ 2-8)
=-32S^2+25
≥0
S≤5√2/8
The maximum area of Δ AOB (o is the origin) is 5 √ 2 / 8

Let the line L and the ellipse C: x ^ 2 / 3 + y2 = 1 intersect at two points, and the distance from the origin o of the coordinate to the line L is √ 3 / 2

First of all, you need to use the chord length formula of straight intersection ellipse, and then after a series of operations, get the root sign (1 + K Square) * | x1-x2|

How many integers have absolute values greater than 1 but less than 3?
What are the integers with absolute values greater than 1 but less than 3?
Urgent need! ~ everybody help! ~ give you bonus points!
Hurry, hurry! ~What are the integers with absolute values greater than 1 but less than 3?
thank you!!!!!!

There are two integers whose absolute value is greater than 1 but less than 3

PEP sixth grade primary school mathematics lecture

"Understanding of tons" is the teaching content of the third section of unit 3 "understanding of kilometers and tons" in Volume 6 of the six-year primary school mathematics textbook for nine-year compulsory education

Put 100 apples in 5 boxes. The number of apples in each box should have the number "6". How to put them

There are other ways to put 16 boxes in 3 boxes, 26 boxes in 2 boxes, but the premise is to take out 30 boxes and put them into 5 boxes in 5 parts, and put the other 70 boxes into 5 boxes in a group of 10. Five boxes can be put completely or not. There are several ways to use permutation and combination

Why is one mu equal to 60 square feet? Please give me the exact reason······

One hour is divided into 60 portions. Each portion is called a second
In the same way, one mu is divided into 60 parts, and one is called one square foot
If you want to ask why you want to divide it into 60 parts, it's not too big and easy to calculate
If you look at 1 second, it's not long or short. And it's 60 integers, which is convenient for calculation
The landlord is a good classmate who is easy to ask
Every attention is learned, and everything in the world has its reason

You have to make it clear to me all the things that solve problems
Fill in the blanks:
1. The length is 36 cm square and rectangle, the width of the rectangle is one fifth of the length, the area of the rectangle is () of the square area
2. There are three continuous even numbers, of which the smallest is six seventh of the largest. These three continuous even numbers are (), (), ()
Calculation problem
(can be simple and easy)
7 / 41 times 1 / 31 + 34 / 31 divided by 31
solve equations:
5 / 7x-5 times 2 / 5 = 8
1. There is a peach tree on the top of a mountain. A monkey ate 1 / 10 of the peaches on the tree on the first day, and then ate 1 / 9 and 1 / 8 of the existing peaches on the next two days. There are still 70 peaches left on the tree. How many peaches are there on the tree?
2. There are 174 students in the sixth grade and 206 students in the fifth grade. The total number of students in the two grades just accounts for 1 / 3 of the total number of students in the school. How many students are there in this school? (use the solution equation and calculate the solution. Both are required.)
3. A project. If a single share is completed, it will take 6 hours for Party A and 8 hours for Party B. If Party A works for 2 hours first and then Party B works together, how many hours did party a work for when the task was completed?
4. Xiao Dong read a story book. One day, he read 1 / 8 of the total pages of the book, which is 21 pages more. The next day, he read 1 / 6 of the total pages of the book, which is 4 pages less, and there are 102 pages left?

Fill in the blank 1 the four sides of a square are equal, so the volume of the square is 36 x 36 = 1296 square meters, the width of the rectangle is one fifth of the width of the song, so it is 36 / 5 = 7.2, the area of the rectangle is 36 x 7.2 = 259.2, the area of the rectangle is the area of the square, that is, the area of the rectangle divided by the area of the square, so it is 259.2 divided by

The altitude of land a is h m, that of land B is 20 m higher than that of land a, and that of land C is 30 m lower than that of land a

B: (H + 20) m, C: (h-30) m, (H + 20) - (h-30) = H + 20-h + 30 = 50 (m), a: the height difference between B and C is 50 m

Fill in the brackets with a greater than or less than sign 5 cubic centimeter 12 cubic decimeter () 5.12 cubic meter 1200 cubic decimeter () 1200 liter 3 meter 5 decimeter () 350 cm
7.05 tons () 7005kg

5 cubic centimeter 12 cubic decimeter (<) 5.12 cubic meter
1200 cubic decimeter (=) 1200 liter
3.5 decimeter (=) 350 cm
7.05 tons (>) 7005kg

I: it is known that ∠ α and ∠ β are obtuse angles. The calculation results of students a, B, C and D are 72 degrees, 90 degrees, 26 degrees and 50 degrees respectively. Which student's calculation result is correct? And write down the reasons
II: two straight lines intersect at a point to form two pairs of vertex angles (less than the flat angle); three straight lines intersect at a point to form six pairs of vertex angles; four straight lines intersect at a point to form twelve pairs of vertex angles And so on
(1) How many pairs of vertex angles do five straight lines intersect at one point?
(2) How many pairs of vertex angles do 100 straight lines intersect at one point

The first question: from the question, we can get that ∠α + ∠β calculated by a is 72 × 6 = 432, B is 90 × 6 = 540, C is 26 × 6 = 153, D is 50 × 6 = 300, and because ∠α and ∠β are obtuse angles, that is, the degree of ∠α must be greater than 90 and less than 180, and the degree of ∠β must be greater than 90 and less than 180, So the degree of ∠α + ∠β must be greater than 180 and less than 360. So only Ding's result 300 is between 180 and 360. So Ding is correct
The second question: through "two straight lines intersect at a point to form two pairs of vertex angles (the angle less than the flat angle); three straight lines intersect at a point to form six pairs of vertex angles; four straight lines intersect at a point to form twelve pairs of vertex angles", we can get a relation y = x × (x-1) (x is greater than or equal to 2 and X is an integer), We can get the relation between X and y, y = x × (x-1), then we can take 5 and 100 into it