The curve represented by equation 4x * X-Y * y + 4x + 2Y = 0 is? The answer is two days intersect but not vertical line!

The curve represented by equation 4x * X-Y * y + 4x + 2Y = 0 is? The answer is two days intersect but not vertical line!

4X^2+4X+1=Y^2-2Y+1
(2X+1)^2=(Y-1)^2
(1)2X+1=Y-1
(2)2X+1=1-Y
(1)Y=2X+2
(2)Y=-2X
Because K1 * K2 is not equal to - 1, and K1 is not equal to K2
So two lines intersect and are not perpendicular

Equations (2x + y) (x + Y-3) = 0 and (4x + 2Y + 1) (2x-y + 1) = 0
(2x+y)(x+y-3)=0
2x+y=0
x+y-3=0
(4x+2y+1)(2x-y+1)=0
4x+2y+1=0
2x-y+1=0
2X + y = 0 is parallel to 4x + 2Y + 1 = 0. There is no intersection point and there is an intersection point with 2x-y + 1 = 0
X + Y-3 = 0 has an intersection with 4x + 2Y + 1 = 0 and 2x-y + 1 = 0
So there are three intersections. I want to know why there are no intersections for 2x + y = 0 and X + Y-3 = 0, 4x + 2Y + 1 = 0 and 2x-y + 1 = 0?

You need to satisfy two equations at the same time!
2X + y = 0 and X + Y-3 = 0 have intersection points, but the solution does not satisfy the equation (4x + 2Y + 1) (2x-y + 1) = 0!
Similarly, 4x + 2Y + 1 = 0 and 2x-y + 1 = 0 have intersection points, but the solution does not satisfy (2x + y) (x + Y-3) = 0
Therefore, it is necessary to find the intersection point between one formula and another, so that two equations are satisfied
If you don't understand, you can ask,

Find the linear equation of the curve 4x ^ 2 + 9y ^ 2-8x + 18y = 59 which is tangent to the line 3x-2y = 6

Let the equation of the straight line be y = KX + B
If two straight lines are vertical, the slopes are negative reciprocal. Then k = - 2 / 3
The equation is y = - 2 / 3 x + B
Bring it into the curve
4x^2+9(-2/3 x+b)^2-8x+18(-2/3 x+b)=59
Because it is tangent, there is only one. Then Δ = 0
Sorted 9b ^ 2 + 18b-127 = 0
B = - 1 + 2 √ 34 / 3 or B = - 1-2 √ 34 / 3

One side of the parallelogram is 3, the other side is 5, and the diagonal is 6. Find another diagonal

Using the second cosine theorem, if COSC = - 1 / 15 is obtained for the first time, then the cosine value of its complement angle (set as ∠ d) is 1 / 15. Using the second cosine theorem, another diagonal is 4 times root sign 2

Solving the equation '(x + 3) (x-1) = 12' to find x

（x+3）（x-1）=12
x²+2x-3=12
x²+2x-15=0
(x+5)(x-3)=0
X = - 5 or x = 3

The tangent of y = f (x)) at (2, f (2)) is y = 2x-1 function, G (x) = x & # 178; + F (x) is tangent equation at (2, G (2))

The tangent of y = f (x)) at (2, f (2)) is y = 2x-1 = 2 (X-2) + 3
∴f′(2)=2 f(2)=3
∵g′(x)=2x+f′(x)
∴g′(x)=4+2=6 g(2)=4+3=7
The tangent equation of function g (x) = x & # 178; + F (x) at (2, G (2)):
y=6(x-2)+7=6x-5

Is there the largest positive number and the smallest negative number in the rational number? Is there the largest negative integer and the smallest positive integer? If so, how many are each?

No
The largest negative integer is - 1, and the smallest positive integer is 1

If the equation x ^ 4-2ax ^ 2-x + A ^ 2-A = 0 has two real roots, then the value range of real number a is? Line, etc
If the equation x ^ 4-2ax ^ 2-x + A ^ 2-A = 0 has two real roots, then the value range of real number a is?

From x ^ 4-2ax ^ 2-x + A ^ 2-A = 0
It is concluded that: (x ^ 2-A) ^ 2 = x + a
Square root: | x ^ 2-A | = (x + a) ^ (1 / 2)
Let f (x) = | x ^ 2-A |, G (x) = (x + a) ^ (1 / 2), the original problem is equivalent to the value of a where f (x) and G (x) have two intersections in the domain of definition
There are three types of cases
(1) When a = 0, then f (x) = x ^ 2, G (x) = x ^ (1 / 2), obviously there are two intersections (0,0) and (1,0), which are in line with the meaning of the problem;
(2) When a = 0 power function curve. This kind of power function curve has a special connection with the straight line y = x, which is an important boundary between the exponent of power function greater than 1 and less than 1, we can investigate the intersection of two curves y = x, which can be divided into the following cases:
(i) When a = - 1 / 4, we can deduce that f (x) and the line y = x are tangent to the point (1 / 2,1 / 2), and G (x) and the line y = x are tangent to the point (1 / 2,1 / 2), then we can deduce that f (x) and G (x) are tangent at this time, and there is only one intersection point, which is not in line with the meaning of the problem;
When AA > -1 / 4, f (x) and line y = x intersect two intersection points, namely (1 / 2 + 1 / 2 root (1 + 4a), 1 / 2 + 1 / 2 root (1 + 4a), 1 / 2 + 1 / 2 root (1 + 4a), 1 / 2-1 / 2 root (1 + 4a), 1 / 2-1 / 2 (1 + 4a), 1 / 2-1 / 2-1 / 2-1 / 2 root (1 + 4a), 1 / 2 + 1 / 2 (1 + 2 + 1 / 2 / 2 + 1 / 2 / 2 / 2 (1 + 4a), 1 / 2 + 1 / 2 + 1 / 2 + 1 / 2 / 2 / 1 / 2 + 1 / 2 (1 + 4a), 1 / 2 + 2 + 1 / 2 + 1 / 2 + 1 / 2-1 / 2-1 (1 + 2-1 + 4a), 1 / 2-1 / 2-1 / 2-1 / 2-1 + 2-1 / 2-1 + 4a, 1 / 2-1 / 2-1 / 2 it's not easy;
(3) When a > 0, then f (x) = | x ^ 2-A |, G (x) = (x + a) ^ (1 / 2), f (x) is a power function curve with opening upward, y = x ^ 2-A and y = 0 in the image, and the intersection points with X axis are a (- radical a, 0) and B (radical a, 0), and the vertex on Y axis is C (0, a); while g (x) is a power function curve with opening right, vertex D (- A, 0), Y > = 0
(i) When point D is between a and origin o, that is: - root a

Nine fifths of 27 is three fourths of a number, and the reciprocal of this number is

9 / 5 of 27: 27 × 9 △ 5 = 243 / 5
243/5=3a÷4,a=243/5
1 / a = 5 / 243 (5 / 243)

The equation of the line perpendicular to the line 3x-4y-7 = 0 and the distance from the origin is 4 is?

The slope of 3x-4y-7 = 0 is 3 / 4
So the slope of the vertical line is - 4 / 3
Let the equation of the line be: 4x + 3Y + a = 0
also
It's 4 away from the origin, so
4=|a|/√4²+3²
=|a|/5
A = 20 or - 20
therefore
The straight line is:
4x+3y+20=0
or
4x+3y-20=0