It is known that the polar coordinate equation of a straight line is θ = π - 4, which intersects with the curve {x = 1 + 2cosa y = 2 + 2sina} at a B to find the length of ab

It is known that the polar coordinate equation of a straight line is θ = π - 4, which intersects with the curve {x = 1 + 2cosa y = 2 + 2sina} at a B to find the length of ab

1. The polar coordinates are transformed into standard rectangular coordinates. The coordinate equation of the straight line is y = x, and the coordinate equation of the curve is (x-1) ^ 2 + (Y-2) ^ 2 = 4, that is, the circle with (1,2) as the center and radius r = 2
2. According to the distance formula from the point to the line, the distance s from the center of the circle (1,2) to the AB line is (2-1) / [(1 ^ 2 + 1 ^ 2) ^ 1 / 2] = [(2) ^ 1 / 2] / 2
3. According to the graphic relationship between line and circle, (1 / 2 * AB) ^ 2 = R ^ 2-s ^ 2
4. Substituting data: ab = (14) ^ 1 / 2
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Change the polar equation psina ^ 2 = 2cosa into a common equation? I hope you can be more detailed,
It is known that the pole of polar coordinate system is at the origin of rectangular coordinate system, and the polar axis coincides with the positive half axis of X axis
Using the transformation formula of polar coordinates and rectangular coordinates
pcosa=x,psina=y
∵ psin²a=2cosa
Multiply both sides by P
∴ (psina)²=2pcosa
The ordinary equation is Y & # 178; = 2x
P. Q is the point on the straight line x = 1 + 4 / 5t, y = 1 + 3 / 5t (t is the parameter) and the curve C: P = √ 2cos (θ + π / 4), then the minimum value of PQ is
9-5√2/10
The general equation of straight line is: 3x-4y + 1 = 0
The general equation of the curve is: X & # 178; + Y & # 178; = X-Y, that is: [x - (1 / 2)] &# 178; + [y + (1 / 2)] &# 178; = (1 / 2)
Then the minimum value of PQ represents the minimum distance from a circle to a straight line
If the distance from the center of the circle to the straight line is 9 / 10 and the radius of the circle is r = √ 2 / 2, then the minimum value of | PQ | is (9 / 10) - (√ 2 / 2) = (9-5 √ 2) / 10
Given the curve C {x = 2cos θ, y = √ 3sin θ (θ is a parameter)}, and the straight line L: y = X-1, what is the length of the chord AB cut by the curve C
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Simple math problems in grade five of primary school
1.（25×4）+（25×6） 2.5×7×10×6
=25×（4+6） =（5×6）×（7×10）
=25×10 =30×70
=250 =210
On Sunday, Xiao Li invited six friends
When she comes to her home, she chooses a box of milk packed in cuboid to entertain her friends. After pouring a full cup for each good friend, does she still have milk? The milk box is 12 cm long, 6 cm wide and 15 cm high. The cup is cylindrical, 8 cm high and has a bottom area of 20 square cm
Cup volume = 8 * 20 = 160 cubic centimeter, 7 people need 1120 cubic centimeter
Milk volume = 12 * 6 * 15 = 1080 cubic centimeter. It takes 960 cubic centimeter to reach six cups, and 120 cubic centimeter more. Xiaoli still has milk. Math problems are not enough, and life can not be full,
Xiao Wang's house is decorated. He goes to the store to buy light bulbs. At the counter of the store, there are 100 watt incandescent lamps and 40 Watt energy-saving lamps. Their unit prices are 2 yuan and 32 yuan respectively. It is known that the lighting effect and service life of these two kinds of lamps are the same. It is known that the electricity price of Xiao Wang's house is 0.5 yuan per kilowatt hour. When the service life of the two kinds of lamps exceeds how long, Xiao Wang will choose Energy saving lamp is cost effective? (electricity consumption (KWH) = power (kw) × time (H)
If the service life of these two kinds of lamps is more than 1000 hours, it is worthwhile for Xiao Wang to choose energy-saving lamps
The current of the calculator is very small, about 100 μ a, which is how much a
0.0001A
Mom bought a piece of color paper 50 cm long and 35 cm wide. How many circles can you cut with this piece of paper with a radius of 8 cm?
It's 1884 meters from Lili's home to the bookstore. Lili goes to the bookstore by bike. How many minutes does it take for Lili to go from home to the bookstore by bicycle according to 100 turns per minute? (the diameter of the bicycle is 0.6 meters)
Write the formula!
Mom bought a piece of color paper 50 cm in length and 35 cm in width. How many circles can you cut with this paper with a radius of 8 cm? The diameter is 8 × 2 = 16 (CM). The length can be cut by 50 △ 16 = 3 (piece) (tail removal method). The width can be cut by 35 △ 16 = 2 (piece) (tail removal method). The maximum can be cut by 3 × 2 = 6 (piece)
What day do you want to visit the museum? Xiao Hong's mother works for 4 days and has 1 day off. Xiao Hong's father works for 2 days and has 1 day off. Xiao Hong has Saturdays and Sundays off. Xiao Hong, her mother and her father work for 2 days; Xiao Hong, her mother and father will have a rest on July 3. They will go to see their grandfather together. They will visit the museum on the next day when they have a rest at the same time. What's the date of visiting the museum?
The least common multiple of 3 and 5 is 15, 2 + 15 = 17, July 17 is Sunday, that is, they have a rest to visit the museum on July 17