Emergency help: in polar coordinate system, what is the length of a tangent line passing through the leading circle of point a (4, - Wu / 2) ρ = 4sin θ

Emergency help: in polar coordinate system, what is the length of a tangent line passing through the leading circle of point a (4, - Wu / 2) ρ = 4sin θ

ρ=4sinθ
ρ^2=4ρsinθ
x^2+y^2=4y
x^2+(y-2)^2=4
The center of the circle is (0,2)
Point a (4, - π / 2)
A (0, - 2)
If the distance from point a to the center of the circle is 4, then the tangent length = root sign (4 ^ 2 + 2 ^ 2) = 2 root sign 5

Polar coordinate curve ρ = θ, rectangular coordinate form of normal equation at the corresponding point of θ = π

This is Archimedes spiral, √ (x ^ 2 + y ^ 2) = arctan (Y / x), implicit function derivation, (1 / 2) (x ^ 2 + y ^ 2) ^ (- 1 / 2) * 2x + (1 / 2) (x ^ 2 + y ^ 2) ^ (- 1 / 2) * 2Y * dy / DX = (1 / x) (dy / DX) / [1 + (Y / x) ^ 2] + Y / (- x ^ 2) / [1 + (Y / x) ^ 2] x / √ (x ^ 2 + y ^ 2) + y * (dy / DX) / √ (x ^ 2 + y ^ 2) = x * dy / DX / (x ^

The polar coordinate equation of the curve ρ = 4sin θ is transformed into rectangular coordinate equation ρ = 4sin θ______ ．

The original polar coordinate equation ρ = 4sin θ is changed into: ρ 2 = 4 ρ sin θ, and the rectangular coordinate equation is changed into: x2 + y2-4y = 0, that is, X2 + (Y-2) 2 = 4. So the answer is: x2 + (Y-2) 2 = 4

If the polar coordinate equation of a curve is ρ = 4cos (θ - π / 3), then its corresponding rectangular coordinate equation is

ρ = 4cos (θ - π / 3) is expanded to be: ρ = 2cos θ - 2 √ 3sin θ, and both sides of the equation are multiplied by ρ at the same time to get ρ ^ 2 = 2 ρ cos θ - 2 √ 3 ρ sin θ; because
If ρ ^ 2 = x ^ 2 + y ^ 2, ρ cos θ = x, ρ sin θ = y, then x ^ 2 + y ^ 2 = 2x-2 √ 3Y, that is, (x-1) ^ 2 + (y + √ 3) ^ 2 = 4

Given that there are two points AB on the number axis, the distance between AB is 1, the distance between a and the origin o is 3, find all the points B and the origin o that meet the conditions

The distance from point a to point O is 3. If the distance between point B and origin o is x, then | x-3 | = 1 can be satisfied, so x is 2 or 4, that is, the distance between point B and origin o is 2 or 4

There are two points AB on the knowledge axis, the distance between a and B is 1, and the distance between a and origin 0 is 3. Then what is the sum of the distances between B and origin 0

A may be at + 3 or - 3, so B may be at - 2, - 4, 2, 4
So the sum is 2 * (2 + 4) = 12

Given that there are two points a and B on the number axis, the distance between a and B is 1, and the distance between a and the origin is 3, what is the sum of the distances between all the points satisfying the conditions and the origin?

A = plus or minus 3; b = 2 or 4 when a = 3; b = - 2 or - 4 when a = - 3; so the sum of distance from the far point is 18

A positive number whose distance from the origin is less than 3.2 on the number axis is? A point whose distance from the origin is equal to 2 on the number axis is?

On the number axis, the positive integers whose distance from the origin is less than 3.2 are 1, 2 and 3; on the number axis, the points whose distance from the origin is equal to 2 represent - 3 and 1

It is known that there are two points a and B on the number axis, the distance between a and B is 1, and the distance between a and origin o is 3. So what is the sum of the distances between all the points B satisfying the conditions and origin 0?

Let the rational number represented by point a be x, and the rational number represented by point B be y, because the distance between point a and origin 0 is 3, that is, | x | = 3, so x = 3 or x = - 3, and because the distance between a and B is 1, so | Y-X | = 1, that is, | Y-X | = ± 1, substitute x = ± 3 into the satisfaction problem. There are four kinds of rational numbers represented by point B: Y1 = - 4, y2 = - 2, Y3 = + 2, Y4 = + 4 It is: | 4 | + | 2 | + | - 2 | + | - 4 | = 12

The distance between a and B points on the number axis from the origin is 2 and 3 respectively, then the distance between ab points is______ ．

∵ the distance between a and B points on the number axis from the origin is 2 and 3 respectively. We can get that point a represents ± 2 and point B represents ± 3. When points a and B are on the same side of the origin, ab = | 3-2 | = 1; when points a and B are on different sides of the origin, ab = | - 2-3 | = 5