Find the linear equation tangent to the curve 4x ^ 2 + 9y ^ 2-8x + 18y = 59 and perpendicular to the straight line 3x-2y = 6

Find the linear equation tangent to the curve 4x ^ 2 + 9y ^ 2-8x + 18y = 59 and perpendicular to the straight 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

To translate the function to the image of y = 2x + 3 is to find the function relation of the translated line through the point (2, - 1),

Y = 2x + 3,
therefore
The slope does not change
Let y = 2x + B
-1=4+b
b=-5
y=2x-5

If the image of the line y = 2x-1 is translated so that the translated image passes through the points (2,7), then the function relation of the evaluated line is__________
3Q pull

y=2x+3
Because translation does not change the value of K, it only changes the value of B
So let y = 2x +? Be (2,7), so? = 3

Increasing interval of function f (x) = 2x ^ 2-inx

The derivation of function
f'(x)=4x-1/x
4x-1/x=0
x1=0.5,x2=-0.5
Because x > 0
So x = 0.5
When x > 0.5, f '(x) > 0
Monotone increasing interval is [0.5, positive infinity]

For a straight parabola y = x & # 178; - 8x + 3, find (1) its vertex coordinates and symmetry axis (2) its intersection coordinates with X axis and Y axis

∵y=x²-8x+3
=(x-4)²-13
(1) the vertex coordinates are (4, - 13), and the axis of symmetry is a straight line x = 4
(2) Let y = 0, we get X & # 178; - 8x + 3 = 0, and the solution is: X1 = 4 + √ 13, X2 = 4 - √ 13;
The coordinates of its intersection with the x-axis are (4 + √ 13,0), (4 - √ 13,0)
Let x = 0 and y = 3, so the coordinates of the intersection of X and y are (0,3)

For a quadratic equation of two variables, the axis of symmetry is
Y = ax ^ 2 + BX + C, then what is the axis of symmetry?
I don't want the vertex formula

x=-b/2a

The sum of two prime numbers is 39, and their product is 74. What is the difference between them?
It's due tomorrow,

The two prime numbers are 2 and 37 respectively, so the difference is 35

If two straight lines 3ax-y-2 = 0 and (2a-1) x + 5ay-1 = 0 pass through points a and B respectively, then the distance AB?

3ax-y-2 = 0 over fixed point (0, - 2)
(2a-1)x+5ay-1=0
2ax-x+5ay-1=0
a(2x+5y)-x-1=0
x=-1
2x+5y=0 ,y=2/5
2ax-x + 5ay-1 = 0 over fixed point (- 1,2 / 5)
AB = radical (1 ^ 2 + 144 / 25) = radical (169 / 25) = 13 / 5

Decompose the following formulas into factors 1. A & # 178; X & # 178; + 16ax + 642.25 (x + y) &# 178; - 16 (X-Y) &# 178;
(1)a²x²＋16ax＋64 (2)25﹙x＋y﹚²－16﹙x－y﹚² (3)x²－6x＋9－y²
(4)(a²＋b²－1)²－4a²b²

1. (AX + 8) & # 178; 2.9 (x + y) (x-9y) 3. (x-3 + y) (x-3-y) 4. (a + b) 4-1

-The value of 6x-y-7x + 6x-2y-10x + 8y + X + 6x-8y

Equal to. - 3y-10x