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Point P is on the vertical bisector of line AB, PA = 7, then Pb=______ ．
∵ point P is on the vertical bisector of line AB, PA = 7, ∵ Pb = PA = 7, so the answer is: 7
Point P is on the vertical bisector of line AB, PA = 7, then Pb=______ ．
∵ point P is on the vertical bisector of line AB, PA = 7, ∵ Pb = PA = 7, so the answer is: 7
It is known that a (- 2,3), B (3,1) and P are on the x-axis. If the length of PA + Pb is the smallest, then the minimum is___ If the length of pa-pb is the largest, the maximum value is___ ．
(1) Find the minimum value: as shown in the figure: make the symmetric point B 'of point B about the X axis, connect ab', intersect the X axis at the point P, ∵ B and B 'symmetries, ∵ Pb = Pb ′, ∵ AP + BP = PA + B' P. according to the shortest line segment between the two points, we can know that point P is obtained. ∵ known a (- 2,3), B (3,1), ∵ B 'coordinates are (3, - 1)
It is known that point P of a (- 2.3) B (3.1) is on the x-axis and the length of pa-pb is the largest
The solution point P must be at the intersection of line AB and X axis
The equation of line AB y = - 2 / 5x + 11 / 5
Let y = 0, that is, x = 11 / 2
Point P (11 / 2,0)
RELATED INFORMATIONS
- 1. Know a (2,1), B (1,3), find a point P on the x-axis, so that the value of PA + Pb is the minimum, then what is the minimum value?
- 2. Given the straight line L: 2x-y + 1 = 0 and the point a (- 1,2) B (0,3), try to find a point P on L, so that the value of PA = Pb is minimum, and find the minimum value
- 3. Given the points a (- 2,5) and B (2,4), find a point P on the straight line L: 2x-2y + 1 = 0, so that | PA | + | Pb |, and find the minimum value
- 4. Given the points a (- 1,0), B (1,0), P is the moving point on the line 2x-y + 1 = 0. (1) when the vector PA * and the vector Pb take the minimum value, we find the coordinates of the op vector and Co And find the value of COS angle APB (2) if P satisfies PA + Pb = pa-pb, the coordinates of P
- 5. It is known that two points a (- 5,2) and B (- 1,7) in the rectangular coordinate plane can find point P on the coordinate axis, so that point PA = Pb
- 6. Given that the two points in the Cartesian coordinate plane are a (2,2), B (- 1, - 2), P is on the X axis, and PA = Pb, the coordinates of point P are obtained
- 7. Point Q moves on the curve X ^ 2 + y ^ 2 = 1, and the symmetric point of point Q about point a (1, - 1) is p. find the trajectory equation of P
- 8. The fixed point a (3,0) is a point outside the circle x ^ 2 + y ^ 2 = 1, P is a moving point on the circle, the bisector of ∠ POA intersects Pa at Q, and the trajectory of Q point is obtained
- 9. From fixed point a (3,0) to fixed circle x ^ 2 + y ^ 2 = 2, make a straight line intersecting circle at point P, and find the trajectory equation of the midpoint of line AP
- 10. The equation of circle C (x-1) ^ 2 + y ^ 2 = 9, point P is a moving point on the circle, the coordinate of fixed point a is (a, 0), and the vertical bisector of line AP and straight line CP intersect at point M (1) If a = - 1, find the trajectory equation of point M; (2) When a changes, try to discuss the type of locus of point M
- 11. PA, Pb and PC are three rays starting from point P. the angle between each two rays is 60 degrees. Then the cosine of the angle between PC and PAB is () A. 12B. 22C. 33D. 63
- 12. We know that the line AB = 8, and there is a point P on the plane. (1) if AP = 5, what is Pb equal to, P is on the line AB?
- 13. PA, Pb and PC are three rays from P, and the angle between each two rays is 60 degrees. So what is the cosine of the angle between PC and PAB? Which is the angle between PC and PAB and why A proof of the angle between line PC and plane PAB
- 14. If PA = 8, Pb = 5 and OA: OB = 4: √ 3, then the distance from point P to plane a is equal to
- 15. As shown in the figure, PA ⊸ o is in the plane, AB is the diameter of ⊙ o, C is the point on ⊙ o, and E.F is the point a in the plane PB.PC The following conclusions are given: 1, AF ⊥ Pb; 2, EF ⊥ Pb; 3, AF ⊥ BC; 4, AE ⊥ plane PBC, where the sequence number of the correct proposition is
- 16. P is a point out of plane a. the angle difference between PA, Pb and plane a is π / 4. Their projective lengths in plane are 2 and 12 respectively. The distance from P to plane is
- 17. Why are the same chords complementary to each other? How to prove the complementarity or equality of the circle angles of the same chord?
- 18. If a chord of a circle is known to divide the circle into two parts of 1:3, then the degree of the angle of the circle to which the chord is directed is______ ．
- 19. A chord is divided into two parts: 1:4. Find the degree of the circumference angle of the chord
- 20. If the distance from the center O to the chord AB is a, then the diameter of O is a