![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
The distance from point P (a, 4) to the straight line x-2y + 2 = 0 is equal to 2 5, and in the plane region represented by inequality 3x + Y > 3, then the coordinates of point P are______ .
A − 2 × 4 + 2|
12+(−2)2＝2
5，
A = 16 or a = - 4
And P (a, 4) is in the plane region represented by inequality 3x + Y > 3,
∴a=16，
∴P（16，4）．
So the answer is (16,4)
In the plane rectangular coordinate system xoy, set up a group of inequalities x-y≤0 2x+y≤0 x-y+2≥0 If ax-y + B ≤ 0, the plane region represented is d. if the boundary of D is diamond, then AB = () A. -2 Ten B. 2 Ten C. 2 Five D. -2 Five
By constraints
x-y≤0
2x+y≤0
x-y+2≥0
The feasible region of ax-y + B ≤ 0 is shown in the figure,
In order to make the quadrilateral obca of feasible region to be diamond, then ax-y + B = 0 is parallel to 2x + y = 0, and | ob | = | OA |,
Then a = - 2,
simultaneous
x-y+2=0
2X + y = 0, B (- 2)
3，4
3），
simultaneous
x-y=0
Ax-y + B = 0, a (b) is obtained
1-a，b
1-a），
By 2 (b)
1-a)2=(-2
3)2+(4
3) 2, combined with a = - 2, B is obtained=-
10．
∴ab=2
10．
Therefore, B
1. It is known that the region D in the plane rectangular coordinate system xoy is determined by the inequality system x + Y-5 ≤ 0, y ≥ x, X ≥ 1, then z = 2x + y maximum value 2. Given that the eccentricity of the ellipse x 2 / a 2 + y 2 / B 2 = 1 (a > b > 0) is 1 / 2, then the equation of the asymptote of the hyperbola x? A? Y? B? 2 = 1 is?
When x = 2.5, y = 2.5, the maximum value of Z = 2x + y is 7.5
2. When the eccentricity is 1 / 2, a ^ 2: B ^ 2 = 4:3, substituting the hyperbola x? 2 / a? - y? 2 / b? 2 = 1, changing the right 1 into 0, the equation of asymptote is
y=±2√3 /3 x
[if you don't know, ask again; if you are satisfied, I wish you good luck
The region D in the plane rectangular coordinate system xoy is given by the inequality | x + 2 | + | y + 2 | ≤ 2. Then the area of region D is equal to
Case 1: X ≥ - 2, y ≥ - 2
(x+2)+(y+2)≤2
y≤-x-2
It refers to the triangle area surrounded by the line y = - X-2, line x = - 2 and line y = - 2
Case 2: X
Given that x > 0, Y > 0, the proof of x ^ 2 + 4Y + 2 ≥ 2x + 4 root sign Y is proved by basic inequality
prove:
x>0,y>0
∴ x²+1≥2x ①
4y+1≥2√y ②
①+②
That is, x ^ 2 + 4Y + 2 ≥ 2x + 4 root sign y
Point P (a, 4) is in the region represented by inequality 3x + Y-3 > 0, and the distance from the straight line x-2y + 2 = 0 is 2 root sign 5, and find the coordinates of point P
The point P (a, 4) is in the region represented by inequality 3x + Y-3 > 0
3a+4-3>0
a>-1/3
The distance from the point P (a, 4) to the straight line x-2y + 2 = 0 is 2 times sign 5
Substituting the formula of distance from point to line
|A-2 * 4 + 2| / root number 5 = 2 root number 5
A = 16 or - 4
A > - 1 / 3
So a = 16
P（16,4）
The function y = root (- x ^ 2 + 2x + 3) - root (3) defines the image of domain [0,2] counterclockwise around the coordinate origin The image of the domain [0,2] defined by the function y = root (- x ^ 2 + 2x + 3) - radical (3) is rotated anticlockwise about the coordinate origin (α is an acute angle). If the curve obtained is still the image of a function, the maximum value of α is obtained The formula can be converted to circle (x-1) ^2+ (y+ root 3) ^2=4 definition field [0,2] value field [0,2- root 3] When x ∈ [0,2], the image is a part of the circle with (1, root 3) as the center and 2 as the radius above the X axis. The angle of the center of the circle is 60 degrees. When the arc is tangent to the X axis, the curve is still a function image, that is, the rotation angle is 60 degrees When the arc is rotated to be tangent to the X axis, why is the rotation angle 60 degrees? How to calculate it
Y is a function of X, which must be given a value of X, and y has a unique value corresponding to it. If a graph is a function image, it must be for any straight line x = a, and their intersection points can only be 1 or 0
Given the function f (x) = root 3lnx (x > = 1), if its image is rotated anticlockwise around the origin θ (0)
F '(x) = √ 3 / x, because x > = 1, so f' (x)
The image of the function y = SiNx (0 ≤ x ≤ 2 π) is rotated anticlockwise around the origin of the coordinate by θ (0 ≤ θ < 2 π), If the curve C is a function image for every rotation angle θ, then the range of angle θ satisfying the conditions is? ([0, π / 4], [0, π / 4] ∪ [3 π / 4,5 π / 4], [0, π / 4] ∪ [3 π / 4,5 π / 4] ∪ [7 π / 4,2 π), [0, π / 4] ∪ [7 π / 4,2 π))
The derivation of the function y = SiNx: the slope of tangent L1 at (0,0) of Y '= cosx curve K1 = cos0 = 1, the slope angle of π / 4, the slope of tangent L2 at (π, 0) of curve K2 = cos π = - 1, the inclination angle of 3 π / 4l1 ⊥ L2 θ∈ [0, π / 4] can ensure that any point (x, y) on the curve corresponds to the unique y value, θ =
Known functions: ① y = 1 / X; ② y = 5x-1; ③ y = root 2x; ④ y = 2-x / 3; ⑤ y = - x, how many images pass through the origin?
③ ⑤
Take x = 0 and y = 0
RELATED INFORMATIONS
- 1. A line passing through the origin O and the image of the function y = log (8) x It is proved that the point P, Q and origin o are on the same line
- 2. In the function y equal to the root of (x-1) cent (3-x), what is the value range of the independent variable x?
- 3. Let the circle O1. The radius of circle O2 is R1 and R2 respectively. If circle O2 is on the circumference of circle O1, what is the distance between O2 and common chord?
- 4. As shown in the figure, circle O1, circle O2, circle O3 are tangent to each other and O1O2 = 2, o1o3 = 4, O2O3 = 4, find the radius of circle O1, circle O2 and circle O3
- 5. Circle O1 the radius of circle O2 is R.R, the distance between centers of circle is D, and the two circles are outward. Point P moves on circle O1, and point Q moves on circle O2. The maximum of PQ is asked The radius of circle O1 and circle O2 are R.R, D and D respectively. Point P moves on circle O1 and point Q moves on circle O2. What are the maximum and minimum values of PQ and why? I already know the answer. = = if you want to score, please answer it carefully!
- 6. It is known that the three points in the plane rectangular coordinate system are a (1, - 1), B (- 2,5) C (4, - 6) are used to judge whether the passing point a, B and C3 can be in a circle
- 7. In the rectangular coordinate system, the circle with point a (root 3,0) as the center and radius 2 and 3 as the radius intersects the X axis at B, C. and Y axis at D, e.50-
- 8. The vertex coordinates of the triangle are a (2, 2), B (4, 2), C (6, 4). Try to reduce △ ABC so that the corresponding side ratio of △ def and △ ABC is 1:2
- 9. The coordinates of the three vertices of △ ABC are a (1, - 1), B (4, 1) and C (2, 2). When △ ABC is rotated 180 ° around the origin of the coordinates, the coordinates of each vertex of the triangle are as follows______ ，______ ，______ .
- 10. In the rectangular coordinate system, the first order function y = x + m and the inverse proportional function y = m / X intersect point a in the first quadrant, intersect point C with X axis, AB is perpendicular to X axis, perpendicular foot is B, and the area of triangle ABO is 1
- 11. It is known that the distance from the point m (2m + 1,3m-5) to the x-axis is twice that of the Y-axis of the other zone, then M (2m + 1,3m-5) is twice as far as the Y-axis of the other zone=
- 12. The circle P: (x-a) 2 + (y-b) 2 = R2 (R ≠ 0) satisfies the following conditions: (1) the chord length obtained by cutting Y-axis is 2; 2) it is divided into two arcs by x-axis, and the ratio of arc length is 3:1. In all circles satisfying condition ① and ②, the equation of circle is obtained when the algebraic formula a2-b2-2b + 4 is the minimum
- 13. Given that the distance between point P (1-A, 2a-5) and two coordinate axes is equal in plane rectangular coordinate system, the value of a is calculated and the coordinates of point P are determined
- 14. In the plane rectangular coordinate system, the point P is above the x-axis, and the distance from the point P to the y-axis is 1, and op = 2, the coordinates of the point P are obtained
- 15. As shown in figure a.e.b.d on the same line, in the triangle ABC and triangle def, BC = EF, AC is parallel to DF, CB is parallel to Fe Is triangle ABC and triangle def congruent? Why? What is the relationship between AF, DC, segment AF, DC___________ Please explain why
- 16. In the plane rectangular coordinate system, take point a (0,3) and point B (4,0) as the center of the circle, and take 8 and 3 as the radius to make circle a and circle B respectively, and find out the position relationship between the two circles
- 17. In the plane rectangular coordinate system, the coordinates of a point a are (a, b). (1) the distance from a to the origin o is expressed by the quadratic radical; (2) the point B (root 5, - radical 3) is calculated Distance to origin
- 18. If the radius of two circles is 3 and 4, and the distance between centers is 7, then the position relationship between the two circles is () A. Separation B. Exotomy C. Endonuclease D. Intersection
- 19. As shown in the figure, AB is the diameter of ⊙ o, chord CD ⊥ AB is at point E, tangent of ⊙ o is made through point B, and the extension line of AC is at point F. it is known that OA = 3, AE = 2, (1) Find the length of CD; (2) Find the length of BF
- 20. It is known that in the triangle ABC, D and E are on AB and AC respectively. If AD / DB = AE / EC, then the following formula holds true 1、AD/EC=DB/AE 2、AB/DB=EC/AE 3、AD/AB=AE/AC 4、AD/DB=BC/EC reason