Find the linear equation which passes through point (2, - 1) and is tangent to circle (x-1) square + (Y-1) square = 5

Find the linear equation which passes through point (2, - 1) and is tangent to circle (x-1) square + (Y-1) square = 5

By substituting the coordinates of a point into the equation of a circle, we can see that a point on a circle has only one tangent equation
The slope of the line passing through the point (2, - 1) and the center of the circle is (- 1-1) / (2-1) = - 2
Then the slope of the line passing through the point (2, - 1) and tangent to the circle is 1 / 2
Substituting point (2, - 1) into y + 1 = (1 / 2) (X-2)
The equation of tangent line is y = x / 2-2

A mathematical problem about the equation of circle
Circle C1 (x + 3) ^ 2 + (Y-1) ^ 2 = 4, circle C2 (x-4) ^ 2 + (Y-5) ^ 2 = 4, let p be a point on the plane, satisfy: there are infinitely many pairs of mutually perpendicular straight lines L1 and L2 passing through point P, which respectively intersect circle C1C2 and are cut by the circle with chord length, etc., find the coordinates of all points satisfying the conditions

Let point P coordinate be (m, n), the equations of line L1 and L2 are y-n = K (x-m), y-n = - 1 / K (x-m), that is, kx-y + N-km = 0, - X / K-Y + N + m / k = 0, because the chord length of line L1 cut by circle C1 is equal to that of line L2 cut by circle C2, and the radii of two circles are equal

Point a (0,2) is a fixed point in the circle x2 + y2 = 16, and points B and C are two moving points on the circle. If Ba is perpendicular to Ca, find the trajectory equation of the midpoint m, and explain what curve the trajectory is

Point a (0,2) is a fixed point in the circle x2 + y2 = 16, and points B and C are two moving points on the circle. If Ba is perpendicular to Ca, find the trajectory equation of the midpoint m, and explain what curve the trajectory is
The results are as follows
Let m (x, y) be the midpoint of BC
|OM|²=R²-(BC/2)²
Triangle ABC is a right triangle, BC / 2 = am
|OM|²=R²-(AM)²
x²+y²=16-[x²+(y-2)²]
Simplify
x²+y²=16-[x²+(y-2)²]
2x²+y²=16-(y-2)²
2x²+y²=16-(y²-4y+4)
2x²+2y²-4y=16-4
2x²+2y²-4y=12
x²+y²-2y-6=0

30 exercises of factorization (difficult)

Find some factoring questions

1、 Fill in the blanks (1) x2 + 2x-15 = (x-3) (_____ ) (2)6xy-x2-5y2=-(x-y)(_____ ). (3)________ =(x + 2) (x-3); (4) factorization factor x2 + 6x-7=__________ (5) if the polynomial x2 + BX + C can be decomposed into (x + 3) (x-4), then B=_____ , c=_____ (6) if x2 + 7x

Reward: 1: A ^ 2 + B ^ 22: A ^ 4 + B ^ 4

1:a²+b²
=（a+b)²-2ab
=(a+b+√(2ab))(a+b-√(2ab)）
2:a^4+b^4
=(a²+b²)²-2a²b²
=(a²+b²+√2ab)(a²+b²-√2ab)

The results are as follows: 1. It takes the same time for a ship to sail 80 km downstream and 60 km upstream. The velocity of water is known to be 3 km / h
2. Party A and Party B travel from a and B 36 kilometers apart at the same time. When Party A starts from place a and drives for 1 km, he finds that there is something left in place a and returns immediately. After taking the object, he immediately moves from place a to place B. in this way, Party A and Party B just meet at the midpoint of place a and B. It is known that Party A travels 0.5 kilometers more per hour than Party B. the speed of Party A and Party B is calculated

1. Let the speed of the ship in still water be X80 / (x + 3) = 60 / (x-3) 80x-80 * 3 = 60x + 60 * 320x = 3 (80 + 60) x = 21km / h. 2. Let the speed of a be x, then the speed of B be x-0.5 [(36 / 2) + 2 * 1] / x = (36 / 2) / (x-0.5) (20 / x) = 18 / (x-0.5) 20x-10 = 18xx = 5, x-0.5 = 4.5

Application of factorization in grade one of junior high school
From February to April this year, the sales of Mou store continued to decline, and the percentage of monthly decline was X
(1) What are the sales of the mall in March and April?
(2) What is the ratio of April sales to the sum of February and March sales?

1,a(1-x),a(1-x)^2
a(1-x)^2/a(1-x)+a=a(1-x)^2/a(2-x)=(1-x)^2/2-x

(x^2-xy)/(xy-y^2)-(y^2+xy)/(x^2+xy)+(x^2+y^2)/xy
2.(x-2)/x^2/(1-2/x)

(x^2-xy)/(xy-y^2)-(y^2+xy)/(x^2+xy)+(x^2+y^2)/xy
=x(x-y)/(y(x-y))-y(x+y)/(x(x+y))+(x^2+y^2)/xy
=x/y-y/x+(x^2+y^2)/xy
=(x^2-y^2)/xy+(x^2+y^2)/xy
=2x^2/xy
=2x/y

On the factorization problem of grade one in junior high school
The fourth power of Y - the second power of Y
3ax²-3ay²
4X cubic - 8x & # 178; + 4x
a-2a(b+c)+(b+c)²
Decomposition should be thorough

The second power of y4-y = y ^ 2 * (y ^ 2-1) = y ^ 2 (y + 1) (Y-1)
3ax²-3ay²=3a(x^2-y^2)=3a(x+y)(x-y)
4X cubic - 8x & # 178; + 4x = 4x (x ^ 2-2x + 1) = 4x (x-1) ^ 2
a-2a(b+c)+(b+c)²=[a-(b+c)]^2=(a-b-c)^2