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Ellipse X & # 178 / 9 + Y & # 178 / 5 = 1, the line between a point P on the line x = - 9 / 2 and the left focus f intersects the ellipse at two points a and B respectively, if the vector PA = λ AF, Ellipse X & # 178 / 9 + Y & # 178 / 5 = 1, the line between a point P and the left focus f on the straight line x = - 9 / 2 intersects ellipse at two points a and B respectively. If vector PA = λ, vector AF, vector Pb = μ, vector BF, calculate λ + μ
Suppose P is on the x-axis with a special value
If the line L passes through the fixed point P (2,1), if the line L respectively intersects the X axis and the positive half axis of the Y axis intersects the two points AB, when the vector PA * and the vector Pb are the maximum, the equation of the line L is obtained
Let the line Y-1 = K (X-2) and use the image K
P is a point outside the plane of square ABCD, PA = Pb = PC = PD = AB, m, n are points on PA and BD respectively, and PN / MA = 1 / 3 (use vector to answer questions!)
(I) to prove: Mn / / plane PBC; (II) to find the angle between Mn and AD
And the key condition of PN / MA = 1 / 3 has leakage error
The line L passing through the point P (1, - 2) with an inclination angle of 45 ° intersects the ellipse x ^ 2 + 2Y ^ 2 = 8 at two points a and B, and finds the value of | PA | multiplied by | Pb |
The topic is in the parametric equation paper
Let the linear equation be: x = 2 & frac12 / 2T + 1
y=2½/2t-2
Then we take it into the elliptic equation and get the | T1 * T2 | = | PA | * | Pb|
The geometric meaning of the linear parametric equation is the distance to the fixed point (the parameter t is that distance). If t is positive above the fixed point, it is negative below the fixed point,
As shown in the figure, ∠ AOC = 140 ° od bisects ∠ AOC, ∠ AOB is a right angle, find the degree of BOD
(not shown)
Because ∠ AOC = 140 ° OC bisects ∠ AOC
Therefore, AOD = 70 degree
And because ∠ AOB = 90 degree
So ∠ BOD = ∠ AOB - ∠ AOD = 90 ° - 70 ° = 20 °
It is known that: as shown in Fig. 1, ∠ AOB = 70 ° (1) as shown in Fig. 2, OC is a ray in ∠ AOB, OD bisects ∠ AOC, if ∠ BOD = 40 °, calculate the degree of ∠ BOC;
(2) If ∠ BOD = ∠ BOC (∠ BOC ＜ 45 °) and ∠ AOD = half ∠ AOC, please draw a graph and find the degree of ∠ BOC
(1) ∵ - AOB = 70 °, ∵ - BOD = 40 °, ∵ - AOD = ∵ AOB - ∵ BOD = 70 ° - 40 ° = 30 °, ∵ od is the bisector of ∵ AOC, ∵ AOC = 2 ∵ AOD = 60 °,
RELATED INFORMATIONS
- 1. Let the moving line l be perpendicular to the x-axis and intersect with the ellipse x2 + 2Y2 = 4 at two points a and B. P is the moving point on L which satisfies the vector PA multiplied by the vector Pb = 1. The trajectory equation of point P is obtained
- 2. Given that point P is a point on line AB, the length ratio of AP to Pb is 2:3. If AP = 4cm, find the length of Pb and ab
- 3. Given that the line segment AB = a, P is a point on AB, and AP = ((radical 5-1) / 2) * a, find the ratio of AP to Pb, AB to AP, and ask whether the four line segments AP, Pb, AB and AP are equal
- 4. Solve the plane equation of the straight line x + 3 / 3 = y + 2 / - 2 = Z / 1 and X + 3 / 3 = y + 4 / - 2 = Z + 1 / 1
- 5. If a line passes through point m (a, 3) and point n (1, 2), the equation of the line is solved
- 6. The equation of a straight line passing through a point (1,0-2), parallel to the plane 3x + 4y-z + 6 = 0 and perpendicular to the straight line (x-3) / 1 = (y + 2) / 4 = Z / 1 is obtained
- 7. Solve the plane equation which passes through the point m (3,1, - 2) and the straight line la-4 / 5 = B + 3 / 2 = C / 1
- 8. For example, there are two points a (1,0) and B (- 1,0) on the plane of the graph, and the known equation of the circle is (x-3) ^ 2 + (y-4) ^ 2 = 2 ^ 2 Find the maximum area of ABP1 with a point p1 on the circle and find out the area
- 9. There are two points a (- 1,0) and B (1,0) on the plane, and point P is on the circle (x-3) 2 + (y-4) 2 = 4. Find ap2 There are two points a (- 1,0), B (1,0) on the plane, and point P is on the circle (x-3) 2 + (y-4) 2 = 4. Find the coordinates of point P when ap2 + bp2 takes the minimum value The equation of a circle is that the square of (x-3) plus the square of (y-4) equals 4 [2 is the square] What we need is also the square of AP plus the square of BP
- 10. Mathematical problems of plane rectangular coordinate system under seven "Monster eats peas" is a computer game. The symbols in the picture indicate the locations where the "monster" passes successively. If (1,2) is used to indicate the third location where the "monster" passes according to the route indicated by the arrow in the picture, can you show the other locations where the "monster" passes in the same way?
- 11. Hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0) f is the right focus, P is a point on the right branch of the hyperbola, P is above the X axis, and M is a point on the left quasilinear O is the origin of coordinates. OmpF is a parallelogram, | PF | = λ| of | (1) Find the relationship between eccentricity e and λ of hyperbola (2) If | ab | = 12, the hyperbolic equation at this time can be obtained (troublesome steps)
- 12. If the moving point P satisfies Po * Po = PA * Pb, the range of PA and Pb can be obtained A. B is the intersection point of a circle and X axis (Note: the origin of the circle is arbitrary), P is a moving point of the circle. The moving point P satisfies Po * Po = PA * Pb?
- 13. Given that the angle a = 60, P and Q are the moving points on both sides of angle a, if the sum of the lengths of AP and AQ is the fixed value 4, the minimum PQ of the line segment is obtained
- 14. Let p be a moving point on hyperbola x24-y2 = 1, o be the origin of coordinates, and m be the midpoint of line OP, then the trajectory equation of point m is______ ．
- 15. F1 and F2 are the two focal points of hyperbola, F1 is the focal point of parabola y ^ 2 = 4x, hyperbola passes a (- 2,0), B (2,0), find the trajectory equation of F2 Note the explanation of the value range of X Don't you know what to do?
- 16. The hyperbola C: 2x ^ - y ^ = 2 is known. Find the trajectory equation of the midpoint Q of the chord AB passing through the point m (2,1)
- 17. Given the hyperbola x ＾ 2-y ＾ 2 / 2 = 1. The straight line passing through point a (2,1) intersects with the hyperbola at P1 and P2, find the trajectory equation of the midpoint P of line p1p2
- 18. The center is at the origin, and a hyperbolic equation with focus (5,0) passing (4,0) is Please write the specific process
- 19. From a point Q on the hyperbola x2-y2 = 1, the perpendicular of the straight line x + y = 2 is drawn. If the perpendicular foot is n, then the trajectory equation of the midpoint P of the line QN is______ ．
- 20. Let p be the interior point of the directed line p1p2, where P1 (2,3) P2 (8,4) is known and p1p / PP2 = PP2 / p1p2, try to find the coordinates of P Vector is the title, thank you, please write the process