Given a (- 2,0), B (2,0), point C and point d satisfy | AC | = 2, vector ad = 1 / 2 (vector AB + vector AC) (1) Finding the trajectory equation of point d (2) Through point a, make a straight line L to intersect the ellipse with a and B as the focus at two points m and N, the distance from the midpoint of line Mn to y axis is 4 / 5, and the line L is tangent to the trajectory of point D, so the equation of the ellipse can be obtained Especially the second question is so difficult | Math enthusiast | Mathematical art

Given a (- 2,0), B (2,0), point C and point d satisfy | AC | = 2, vector ad = 1 / 2 (vector AB + vector AC) (1) Finding the trajectory equation of point d (2) Through point a, make a straight line L to intersect the ellipse with a and B as the focus at two points m and N, the distance from the midpoint of line Mn to y axis is 4 / 5, and the line L is tangent to the trajectory of point D, so the equation of the ellipse can be obtained Especially the second question is so difficult

Let C (XC, YC), D (x, y), then the trajectory equation of vector AB = (4,0), vector AC = (XC + 2, YC), vector ad = (x + 2, y) ∵|| AC | = 2  C is: (XC + 2) & sup2; + YC & sup2; = 4 (1) ∵ vector ad = 1 / 2 (vector AB + vector AC) ≠ algebraically expressed as: x + 2 = 1 / 2 (XC + 2 + 4) y = 1 / 2yc

RELATED INFORMATIONS

1. Among the following physical quantities, those belonging to vector are: () A. gravity B. distance C. displacement
2. It is known that x, y and Z are three nonnegative integers satisfying 3x + 2Y + Z = 5 and X + Y-Z = 2. If s = 2x + Y-Z, then the sum of the maximum and minimum of S is___ ．
3. It is known that a vector and B vector are not collinear, OA vector = α a vector, OB = β B vector (α, β are not equal to 0). If C is on the line AB, and OC vector = XA vector + Yb vector, we prove that X / α = Y / β = 1
4. As shown in the figure, a middle school has a rectangular site with a length of AM and a width of BM. It is planned to build two mutually perpendicular roads with a width of 2m on the site, and the remaining 4 roads will be built
5. If a = 2m * + 3m-2a-1, B = - M * + am-1 and the value of a + 2B has nothing to do with m, find the value of a (* = 2) if a = 2m * + 3m-2a-1, B = - M * + am-1 and a
6. The area of a rectangle is 24.2 square meters, the length is unchanged, the width is expanded by 5 times, and the expanded rectangle area is ()
7. Cut a 3M long rope into 5 segments, each segment is full court (), is 1m ()
8. Take a 3M long rope and cut it at any position after straightening, then the probability that the length of two sections is not less than 1m is () A. 12b. 13C. 14d. Uncertainty
9. (1.6m * 1m) * 2 + (1.3m * 1m) * 2 + 1.6m * 1.3m = what area?
10. Reduce one side of the square by 30% and increase the other side by 3 meters to get a rectangle, which is equal to the area of the original square______ Square meters
11. As shown in the figure, AC bisector angle bad, CE is perpendicular to ab. (2) when angle ADC + angle ABC = 180 °, 2ae = AB + ad is proved
12. When the linear inequality ax + B of one variable is greater than 0 or ax + B is less than 0 and is a linear function y = ax + B (a is not equal to 0), it can be regarded as the --- of the linear function y = ax + B
13. As shown in the figure, in square ABCD, its side length is 1, P is the midpoint of CD, and point q is on the line BC. When BQ is what value, △ ADP is similar to △ QCP?
14. Let's talk about the meaning difference of each set, the more detailed the better, {x | x = 1}, {y | (Y-1) & # 178;}, {x = 1},
15. P is a point outside the plane ABC of a right triangle, and angle c is a right angle if PA = Pb = PC (1) Determine the position of projection o of point P on plane ABC (2) If AC = 18, the distance from P to the surface ABC is 40, the distance from P to BC is calculated
16. The range of y = log base 1 / 2 index (2a-3)? Please write clearly the process
17. If the radius of the inscribed circle is 1, then the circumference of the triangle is () A. 15B. 12C. 13D. 14
18. Given the points a (5, y), B (1,2), and the vector AB = 5, then y=
19. In △ ABC, ab = AC, D is a point on the extension line of Ca, DF ⊥ BC
20. It is known that a = (1,0) and B = (2,1). When k is the value, ka-b is parallel to a + 3B. When parallel, are they in the same direction or in the opposite direction? (A and B are vectors)