Mathematical problems of circle equation in senior one Find the standard equation of the circle whose center is on the line y = - 4x and tangent to the line a: x + Y-1 = 0 at point P (3, - 2)!

Mathematical problems of circle equation in senior one Find the standard equation of the circle whose center is on the line y = - 4x and tangent to the line a: x + Y-1 = 0 at point P (3, - 2)!

Let the equation of circle center O (m, - 4m) be (x-m) ^ 2 + (y + 4m) ^ 2 = R ^ 2
Then the distance from the center O (m, - 4m) to the straight line a: x + Y-1 = 0 is r
R = | m-4m-1 / radical 2
And P (3, - 2) on the circle: (3-m) ^ 2 + (- 2 + 4m) ^ 2 = R ^ 2
The above two equations are solved simultaneously
M = 1, r = 2 * radical 2
The equation of circle is (x-1) ^ 2 + (y + 4) ^ 2 = 8

1. Given that a circle passes through point a (2, - 1) and is tangent to the straight line x + Y-1 = 0, the center of the circle is on the straight line 2x + y = 0?
2. Solve the tangent equation of a (- 2, - 4) direction circle x2 + y2 = 4
Urgent need——————

(1) Obviously, the point a (2, - 1) is just on the tangent x + Y-1 = 0, so the center of the circle is on the straight line y = x-3 passing through point a and perpendicular to the tangent. The center of the circle is on the straight line 2x + y = 0, so the center of the circle is on the intersection of two straight lines y = x-3,2x + y = 0. Thus, the center of the circle (1, - 2) can be obtained

The nonempty set a = {X / - 2 ≤ x ≤ a}, B = {Y / y = 2x + 3, X ∈ a}, C = {Z | z = x & # 178;, X ∈ a},
B = {Y / y = 2x + 3, X ∈ a}, C = {Z | z = x & # 178;, X ∈ a}, d = {X / - 4-A ≤ x ≤ 2}, if a ∩ d = a, B ∩ C = B, find the value range of A

If a is not empty, then a > = - 2
A is the interval [- 2, a]
B is the interval [- 1,2a + 3]
When - 2=

If the integers a and B satisfy 6ab = 9a-10b + 303, then a + B=______ ．

∵ 6ab = 9a-10b + 303, ∵ (3a + 5) (2b-3) = 288 = 25 × 32, and ∵ A and B are integers, ∵ only 3A + 5 = 25, 2b-3 = 32, ∵ a = 9, B = 6, ∵ a + B = 15

3N ^ 3-1 / 27N (factorization)

3n^3-1/27n =3n(n^2-1/81) =3n(n+1/9)(n-1/9)

1、x(x-y)(x+y)-x(x+y)^2
2、（2a+b)(2a-3b)-3a(2a+b)

1) x(x-y)(x+y)-x(x+y)^2
=x((x-y)(x+y)-(x+y)^2)
=x(x^2-y^2-x^2-2xy-y^2)
=x(-2xy-2y^2)
=-2xy(x+y)
2) （2a+b)(2a-3b)-3a(2a+b)
=(2a+b)(2a-3b-3a)
=(2a+b)(-a-3b)
=-(2a+b)(a+3b)

Four questions on factorization
x^3-5x+4
a^2-4ab+3b^2+2bc-c^2
x^3-4x^2+5x-6
x^4+2x^2-2a-a^2

x^3-5x+4=x^3-x^2+x^2-x-4x+4=x^2(x-1)+x(x-1)-4(x-1)=(x-1)(x^2+x-4)a^2-4ab+3b^2+2bc-c^2=a^2-4ab+4b^2-b^2+2bc-c^2=(a-2b)^2-(b-c)^2=(a-2b+b-c)(a-2b-b+c)=(a-b-c)(a-3b+c)x^3-4x^2+5x-6=x^3-3x^2-x^2+5x-6=x^2(...

Factorization
a³-ab²=?
8x³-72x=?
m³n-9mn=?
x²（a-b）+（b-a）=?

a³-ab²=a(a²-b²)=a(a+b)(a-b)8x³-72x=8x(x²-9)=8x²(x+3)(x-3)m³n-9mn=mn(m²-9)=mn(m+3)(m-3)x²（a-b）+（b-a）=x²(a-b)-(a-b)=(a-b)(x²-1)=(a-b)(x+1)...

Four factorization problems were solved
1.(x^2+x+4)^2+8x(x^2+x+4)+15x^2
2.x^2+(a+b+c)x+(a+b)c
3.x^4+4x^3+4x^2-11(x^2+2x)+24
4.x^4+x^2-2ax+1-a^2

1. (x ^ 2 + X + 4) ^ 2 + 8x (x ^ 2 + X + 4) + 15x ^ 2 = (x ^ 2 + X + 4) ^ 2 + 8x (x ^ 2 + X + 4) + 3x * 5x (using cross multiplication) = (x ^ 2 + X + 4 + 3x) (x ^ 2 + X + 4 + 5x) = (x ^ 2 + 4x + 4) (x ^ 2 + 6x + 4) = (x + 2) ^ 2 * (x ^ 2 + 6x + 4) (Integer Decomposition up to this point) = (x + 2) ^ 2 * (x + 3 - √ 5) (x + 3 + √ 5) 2. X ^ 2 + (...)

Four factorization problems, help solve
①x^2+7x-18；
②x^2-2x-15；
③y^2-8y+15；
④m^2-2m-3.

Solution
x²+7x-18
1 9
1 -2
=(x+9)(x-2)
x²-2x-15
1 -5
1 3
=(x-5)(x+3)
y²-8y+15
1 -5
1 -3
=(y-5)(y-3)
m²-2m-3
1 -3
1 1
=(m-3)(m+1)