Given that the coordinate of point a is (0,1), the coordinate of point B is (2 / 3, - 2), and point P moves on the line y = - x, when the absolute value of PA minus Pb is the maximum, the coordinate of point P is?

Given that the coordinate of point a is (0,1), the coordinate of point B is (2 / 3, - 2), and point P moves on the line y = - x, when the absolute value of PA minus Pb is the maximum, the coordinate of point P is?

A is about the symmetric point a '(- 1,0) of the line y = - X,
Let the analytic expression of the straight line a'B be y = KX + B
0=-K+b
-2=2/3K+b
The solution is k = - 6 / 5, B = - 6 / 5,
∴Y=-6/5X-6/5,
Solve the equations
Y=-6/5X-6/5
Y=-X
X = - 6 / 11, y = 6 / 11,
∴P(-6/11,6/11).

Given that 1 / 3 ≤ a ≤ 1, if f (x) = ax ^ 2-x + 1, the maximum value is m (a) and the minimum value is n (a) in the interval [1,3]
Let g (a) = m (a) - n (a) find the analytic expression of G (a). Find the monotone interval of G (a)

The symmetry axis equation of ∵ function f (x) = ax ^ 2-x + 1 is: x = 1 / 2a, the ∵ function f (x) = ax ^ 2-x + 1 is an increasing function on [1 / 2a, 3], the vertex is: (1 / 2a, 1-1 / (4a)), and the ∵ function g (a) is monotonically increasing on [1 / 3,1]

Given that 1 / 3 ≤ a ≤ 1, if f (x) = ax ^ 2-2x + 1, the maximum value in the interval [1,3] is m (a), and the minimum value is n (a),
Find the expression of M (a) n (a) and the range of M (a) n (a)

Classified discussion
If 1 / 3 ≤ a ≤ 1, then 1 ≤ 1 / a ≤ 3,
Y = ax ^ 2-2x + 1, the equation of axis of symmetry is x = 1 / A, the opening of parabola is upward,
(1) When 1 ≤ 1 / A

Given 1 / 3 ≤ a ≤ 1, find the maximum m and minimum n of the function y = ax ^ - 2x + 1 in the interval [1,3]
When the axis of symmetry is 2, whether the minimum value is 1 / A, the maximum value, take 3, or take 1 in

(1).1/2≤a≤1,====>ymax=y(3)=9a-5,ymin=y(1/a)=(a-1)/a.(2).1/3≤a≤1/2===>ymax=y(1)=a-1.ymin=y(1/a)=(a-1)/a.

As shown in the figure, the square area is 8 square centimeters. How many square centimeters is the painted area?
It's not a three quarter circle. It's a square minus a quarter circle. It's a triangle

Find the minor axis length, eccentricity, focus coordinates and vertex coordinates of the major axis of the following ellipse:
(1)x^2+4y^2=16;
(2)9x^2+y^2=81.

1.x^2/16+y^2/4=1
a=4,b=2,c=2*3^(1/2)
e=c/a=[3^(1/2)]/2,
Focus: (2 * 3 ^ (1 / 2), 0), (- 2 * 3 ^ (1 / 2), 0)
Vertex coordinates: (4,0), (- 4,0), (0,2), (0, - 2)
2.x^2/9+y^2/81=0
a=9,b=3,c=6*2^(1/2)
e=c/a=[2*2^(1/2)]/3
Focus: (0,6 * 2 ^ (1 / 2)),: (0, - 6 * 2 ^ (1 / 2))
Vertex: (3,0), (- 3,0), (0,9), (0, - 9)

The area of the painted part in the figure is 90 square centimeters. What is the area of the smaller square

This is the topic of grade 6 in primary school. We can directly calculate 2x90 = 180 with the transformation method. The specific proof is as follows: the area of the triangle below the coloring part is (a + b) B / 2, and the area of the trapezoid (small trapezoid plus red triangle) in the large square is also (a + b) B / 2. These two areas subtract the area of the small trapezoid at the same time, and the rest is

Find the major axis, minor axis, eccentricity, focus coordinates, and vertex coordinates of the following ellipses
1）x＾2／16＋y＾2／25＝1
2）x＾2＋9y＾2＝81
3）9x＾2＋y＾2＝1

(1) 25 > 16, so focus on Y-axis a ^ 2 = 25, B ^ 2 = 16C ^ 2 = 25-16 = 9, so long axis length = 2A = 10, short axis length = 2B = 8 eccentricity e = C / a = 3 / 5, focus coordinates (0,3), (0, - 3) vertex coordinates (0,5), (0, - 5), (4,0), (- 4,0) (2) x ^ 2 / 81 + y ^ 2 / 9 = 181 > 9, so focus on X-axis a ^ 2 = 81, B ^ 2 = 9C ^ 2 = 81-9 = 72

As shown in the figure, the area of the parallelogram is 20 square centimeters. What is the area of the shadow?

A: the area of the shadow is 2 square centimeters

Let f (x) = sin (2x - π / 6) - m have two zeros in the interval [0, π / 2], then m [1 / 2,1]
Let f (x) = sin (2x - π / 6) - m have two in the interval [0, π / 2], then m [1 / 2,1]

The range of (2x - π / 6) is [- π / 6,5 π / 6]
Then draw the image of SiNx in [- π / 6,5 π / 6]. Observe the image above. When y = m, M is in the range of [1 / 2,1], there are two intersections with the previous image. That is, f (x) has two zeros
We must combine numbers with shapes