![](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>)
Point P is a point outside the line L, a, B, C are three points on the line L, PA = 4cm, Pb = 5cm, PC = 2cm, then the distance between point P and line L () A. Less than 2cm B. Equal to 2cm C. No more than 2cm D. It's 4 cm
∵ according to the distance from the point to the straight line, it is the vertical line segment from the point to the straight line (the vertical line segment is the shortest),
2＜4＜5，
The distance from point P to line L is less than or equal to 2, that is, not more than 2,
Therefore, C
If R and R are the two roots of the equation x2-m (M-4) x + 5-m = 0, then find the value of M
∵ two circles are circumscribed, the center distance is 5, and their radii are R and R respectively,
∴R+r=5，
∵ R and R are the two roots of the equation x2-m (M-4) x + 5-m = 0 with respect to x, respectively,
∴R+r=m（m-4）=5，
M = - 1 or M = 5 (omitted)
∴m=-1．
The radii of two circles are R and R (r > R) respectively, and the distance between centers of two circles is d. if the equation x2-2rx + (R-D) 2 = 0 on X has two equal real roots, then the position relationship between the two circles is () A. Must be inscribed B. Definite circumcision C. Intersection D. Endotomy or exotomy
Because the equation has two equal real roots, the discriminant is equal to 0
Then: △ = (2R) 2-4 (R-D) 2 = 0,
[2r-2（R-d）][2r+2（R-d）]=0
The results show that d = R + R or D = r-r
So two circles are circumscribed or inscribed
Therefore, D
If the radii of the two circles are known to be 1 and 5 respectively, and the center distance of the two circles satisfies d ^ 2-10d + 24 < 0, then the position relationship between the two circles is?
intersect
Given that the radii of the two circles are 1 and 4 respectively, and the distance between the centers of the two circles is 3, then the position relationship between the two circles is ...
Concentric circle is a special kind of inclusion. O1O2 = R1-R2 belongs to inscribe
Given that the radii of two circles are the two roots of the equation x2-3x + 2 = 0, and the distance between the centers of the two circles is 4, then the position relationship between the two circles is______ .
∵ the radius of the two circles is the two roots of the equation x2-3x + 2 = 0,
The sum of the two = 3 = the sum of the radii of the two circles,
And ∵ center distance = 4,4 ᦝ 3,
The two circles are separated from each other
So the answer is to leave
As shown in the figure, in the plane rectangular coordinate system xoy, take the ox axis as the starting edge to make two acute angles α and β, and their final edges intersect with the unit circle at two points a and B respectively Two 10，2 Five 5． (1) Calculate the value of Tan (α + β); (2) Find sin2 α + sin2 α 6 cos 2 α + cos 2 α
Cos α=
Two
10，cosβ=2
Five
Five
∵ α and β are acute angles, ᙽ sin α = 7
Two
10，sinβ=
Five
5，tanα=7，
∴tanβ=1
2，
（1）tan（α+β）=7+1
Two
1−7×1
2=-3．
（2）sin2α+sin2α
6cos2α+cos2α=sin2α+2sinαcosα
7cos2α−sin2α=tan2α+2tanα
7−tan2α=49+14
7−49=-3
2．
As shown in the figure, in the plane rectangular coordinate system xoy, make two acute angles α, β with the ox axis as the starting edge, and their final edges respectively intersect the unit circle at two points a and B. It is known that the abscissa of two points a and B are Two 10，2 Five 5． (1) Calculate the value of Tan (α + β); (2) Find the value of α + 2 β
(1) According to the definition of trigonometric function, cos α =
Two
Ten
，cosβ＝
Two
Five
Five
,
Because α is an acute angle, then sin α > 0, so sin α =
1−cos2α
=
Seven
Two
Ten
Similarly, sin β =
1−cos2β
=
Five
Five
,
Therefore, Tan α = 7, Tan β =
One
Two
.
So tan (α + β)=
tanα+tanβ
1−tanα•tanβ
=
7+
One
Two
1−7×
One
Two
＝−3；
（2）tan（α+2β）=tan[（α+β）+β]=
−3+
One
Two
1−(−3)×
One
Two
＝−1，
And 0 ＜ α
PI
Two
，0＜β＜
PI
Two
Therefore, 0 ＜ α + 2 β ＜
3 pi
Two
,
Therefore, from Tan (α + 2 β) = - 1, α + 2 β = -1
3 pi
Four
.
In the plane rectangular coordinate system xoyo, the ox axis is the starting edge and two acute angles a and B are made. Their final edges intersect two points a and B respectively with the unit circle A. The abscissa of B is the root 2 / 10 and the root 5 / 5 Find Tan (a + b); find a + 2B
Tan (a + b) = minus 3, a + 2b is 135 degrees, don't you need a detailed process
As shown in the figure, in the plane rectangular coordinate system, the point P (0, - 4) moves along the positive direction of the x-axis with a velocity of 1 unit per second, while the point R (16,0) moves in the negative direction of the x-axis with a velocity of 3 units per second, and the movement time is T seconds. (1) if the distance between points P and R is equal, calculate the value of T? (2) if point Q (0,12) moves at the speed of 2 units per second with P and R at the same time, what is the value of T, Is there a double relationship between the area of △ poq and △ ROQ?
(1) Let the velocity of point p be V1, the velocity of point R be V2, and the movement time be t
V1=1 ,V2=3
According to the meaning of the question, 4-v1t = 16-3t, t = 6
(2) What is the direction of Q point, otherwise it is very complicated
RELATED INFORMATIONS
- 1. As shown in Fig. 1, in the plane rectangular coordinate system, point a starts from (1,0) and moves along the x-axis at the speed of 1 unit length per second In the process of motion, the rhombus oabc is made with OA as one side, so that B and C are in the first quadrant and ∠ AOC = 60 ° to connect AC and ob. At the same time, point m starts from the origin O and moves along the diagonal line ob at the speed of three unit length of the root sign per second. If the circle is drawn with point m as the center and Ma as the radius, the movement time is set as T seconds 1. When t = 1, judge the position relationship between point O and circle m, and explain the reason 2. When the circle m is tangent to the OC edge, calculate the value of T 3. With the change of T, the number of common points on the four sides of circle m and diamond oabc is also changing. Please write down the corresponding relationship between the number of common points and the size of T
- 2. In the plane rectangular coordinate system, if the center of circle P (2, a) (a > 2), radius is 2, and the length of chord ab of circle P is two 3, then the value of a is I know the answer is 2 + radical 2, but why
- 3. As shown in the figure, in the plane rectangular coordinate system, the straight line y = 4 / 3x + 8 intersects the coordinate axis at two points a and B, AE bisection angle Bao intersects the Y axis at e, and point C is a point in the first quadrant of the line y = X Find the e-coordinate of the point, AE analytic formula problem supplement: chart
- 4. In the plane rectangular coordinate system xoy, it is known that the circle m with m as the center passes through three points F1 (0, - C) F2 (0, c) a ((√ 3) C, 0), where C > 0 (1) finds the mark of circle M In the plane rectangular coordinate system xoy, it is known that the circle m with m as the center passes through three points F1 (0, - C) F2 (0, c) a ((√ 3) C, 0), where C > 0 (1) Find the standard equation of circle m (expressed by formula containing C) (2) It is known that the left and right vertices of the ellipse y ^ 2 / A ^ 2 + x ^ 2 / b ^ 2 = 1 (a > b > 0) (where a ^ 2-B ^ 2 = C ^ 2) are D, B, and the two intersections of circle m and X axis are a and C respectively, and point a is on the right side of point B, and point C is on the right side of point D. ① calculate the range of eccentricity of ellipse; ② if a, B, m, O, C, D, (o is the origin of coordinates) are uniformly distributed on the X axis in turn, Is the intersection of MF1 and df2 on a fixed line? If so, ask for the equation of the fixed line; if not, please explain the reason
- 5. There are () A. 1 B. 2 C. Three D. Four
- 6. The line y = - 4 3x + 4, x-axis and y-axis intersect at point a and B respectively. In the plane rectangular coordinate system, the distance between a and B points to the straight line a is 2, then the number of lines a satisfying the condition is () A. 1 B. 2 C. 3 D. 4
- 7. In the plane rectangular coordinate system xoy, the intersection points of curve y = xsquare-4x + 3 and two coordinate axes are on circle C. find out the equation of circle C! 2, whether there is a real number a, so that the circle C and the straight line X-Y + a = 0 intersect at two points a and B, and the angle AOB = 90 ° is satisfied. If there is a value of a, if not, explain the reason
- 8. In the plane rectangular coordinate system xoy, the parabola y = ax ^ 2 + BX + C (a ≠ 0) passes through point a (- 3,0) and point B (1,0). Let the intersection point of parabola and Y axis be point C (1), directly write out the symmetry axis of parabola (2) and find the length of OC (expressed by algebraic formula of a)
- 9. As shown in Figure 1, in the plane rectangular coordinate system, the straight line AB intersects X axis at point a, intersects Y axis at point B, and point C is the moving point on line ab (1) If ∠ OAB is 20 ° larger than oba, OC ⊥ AB, calculate the degree of ∠ AOC; (2) As shown in Fig. 2, am bisection ∠ Bao, BM bisection ∠ OBN. When point a moves on the negative half axis of X axis, does the value of ∠ AMB change? If it does not change, calculate the degree of ∠ AMB; if it changes, please explain the reason; (3) As shown in Fig. 3, if ∠ OAB = 45 ° and ∠ OPA = ∠ BPD, ∠ BDP = ∠ ODF, then the following two conclusions are obtained: Please point out that there is only one correct conclusion
- 10. In the plane rectangular coordinate system xoy, there is an ellipse with F1 (0, - radical 3) and F2 (0, radical 3) as the focus and eccentricity as the root 3 / 2. Let the part of the ellipse in the first quadrant be a curve C, the moving point P is on C, the intersection points of tangent of C at point P and X, Y axis are a and B respectively, and vector om = vector OA + vector ob (1) The minimum value of locus equation (2) | vector om | of point m
- 11. If point P is a point outside the line L, ABC is three points above L, PA = 3cm, Pb = 4cm, PC = 5cm, then the distance from point P to line L is? A.3cm B.4cm C. Less than 3cm D. no more than 3cm
- 12. It is known that the radii of the intersecting circles are 5cm and 4cm respectively, and the common chord length is 6cm
- 13. If the radius of ⊙ o is 5cm and the length of chord AB is 6cm, then the distance from the midpoint of chord AB to the midpoint of inferior arc AB is______ .
- 14. What is the chord length of the straight line y = radical 3x cut by the circle x? + y? - 4Y = 0?
- 15. If the radius of ⊙ o is 5cm, and the shortest chord length passing through a point P in ⊙ o is 8cm, then Op=______ .
- 16. If the distance from a point on a straight line to the center of a circle is equal to the radius of the circle, then the straight line is the tangent line of the circle. B. the distance from the center of the circle to the straight line The correct one of the following propositions is () A. If the distance from a point on a line to the center of a circle is equal to the radius of the circle, the line is tangent to the circle B. If the distance from the center of the circle to the straight line is not equal to the radius, the line intersects the circle C. If a line and a circle have a unique common point, the line is tangent to the circle D. If the line AB has no intersection with the circle, then the line AB is separated from the circle PS: I feel both C and D are right~
- 17. How many points on the circle x ＾ 2 + y ＾ 2 + 2x + 4y-3 = 0 to the straight line x ＾ y + 1 = 0 is the root sign 2! Although there are online solutions, but I still don't understand! Please explain!
- 18. It is known that a vertex of an ellipse is a (0, - 1) and the focus is on the x-axis. If the distance between the right focus and the root of the line X-Y + 2 is 2 = 0, the distance is 3 Let the ellipse intersect with the straight line y = KX + m and have different two points m n when am = an to find the value range of M
- 19. (2006 Yantai) known: on the one variable quadratic equation X2 - (R + R) x + 1 4D2 = 0 has no real root, where R and R are the radii of ⊙ O1, ⊙ O2 respectively, and D is the center distance between the two circles, then the position relationship of ⊙ O1, ⊙ O2 is () A. Exotropism B. Tangency C. Intersection D. Contains
- 20. It is known that the straight line L is tangent to the circle C: x square + y square + 2x-4y + 4 = 0, and the distance from the origin o to L is 1, and the equation of the straight line L is obtained