1, known ellipse x? /24+y？ /16= 1, straight line L:x/ 12+y/8= 1, p is a point on l, ray OP and ellipse intersect at point r, point q is on OP, and it satisfies | OQ ||| =| or. When point P moves on L, find the trajectory of point Q.

Let: q (x, y)- > linear OQRP equation be: y = (y/x) x) x.

Where l-> xP=24X/(2X+3Y) and yP=24Y/(2X+3Y).

∵| OQ ||| OP | =| or |? -& gt； xR？ =X？ xP=24X？ /(2X+3Y)，yR？ =24Y？ /(2X+3Y)

And R(xR.yR) is on the ellipse->; x？ /(2X+3Y)+3Y？ /[2(2X+3Y)]= 1

-& gt； 2X？ +3Y？ = 2(2X+3Y)-& gt； 2(X- 1)？ +3(Y- 1)？ =5

-& gt； (X- 1)？ /(5/2)+(Y- 1)？ /(5/3)= 1

2. It is known that O (0 0,0), B (1 0) and C (b, c) are the three vertices of △OBC.

(1) Write the coordinates of the center of gravity G, the outer center F and the vertical center H of △OBC, and prove the * * * lines of G, F and H.

Gravity center g-> xG=(0+ 1+b)/3, yg = (0+0+c)/3-> G( 1+b/3，c/3)

External center f-> xf = (0+1)/2 =1/2.

OC midpoint d (b/2, c/2)->; DF equation: y-c/2=(-b/c)(x-b/2)

Let x = 1/2-> yF=(c? +b？ -b)/(2c)

H-> XH=b, the higher order equation on the side of BC: y = [(1-b)/c] x.

Let x = b-> yH=(b-b? )/c

(2) When the straight line FH is parallel to OB, find the trajectory of vertex C..

FH∨OB-& gt； yF = yH-& gt； (c？ +b？ -b)/(2c)=(b-b？ )/c

-& gt； c？ +b？ -b=2b-2b？ -& gt； 3b？ -3b+c？ =0

-& gt； 3(b- 1/2)？ +c？ =3/4

-& gt； 4(x- 1/2)？ +4y？ /3= 1(x≠ 1/2，y≠0)